Housing prices are often looked as a black box with differing perspectives of the price determination like size of the house, location, and with some even feeling like it's completely random. We, along with a lot of people across the United States, one day envision owning homes making it important for us to get a deeper understanding of the topic. Throughout the process - from dataset collection to conclusion development - we kept in mind considerations that many people can relate to when purchasing a home such as does it feel more expensive to buy a home in summer vs winter or do homes with larger prices have lots of bathrooms. Our dataset was collected on Kaggle.com and has 19(?) features along with the target variable of price sold. We hope that one day housing prices calculations can be as simple as plugging in the values of the features and getting an exact estimate for one's house value. This would enable individuals to optimize for the factors that are the most valuable to them while staying under budget.
We are choosing the Housing Prices Dataset set from Sukhmandeep Singh Brar. This housing price dataset provides a comprehensive collection of property listings, encompassing various attributes such as the number of bedrooms, bathrooms, living area size, lot size, and zip codes, all gathered from house listings in and around Seattle. We found this dataset on Kaggle from the original author.
We’ve chosen this dataset for its large size (2.52 MB) and for the large number of features associated with each house listing, totaling 21 features for each house. It is also localized to a single area (Seattle) which will allow us to extract specific and in-depth insights
Through this dataset, we aim to analyze and determine the effect of various features such as zip code, number of floors, number of bedrooms, square footage, and more on the estimated price of a house.
We are choosing this dataset to understand and analyze which house features best predict the price and which variables affect housing prices most severely. We will leverage several techniques including regression modeling to determine the value of a house based on various input variables.
Source Dataset link: https://www.kaggle.com/datasets/sukhmandeepsinghbrar/housing-price-dataset
As our team used google colab for much of this there are some code cells that account for runs on google colab, however much of the visualization can only be done locally so these cells will be commented out when submitted
#for google colab
#from google.colab import drive
#drive.mount('/content/drive')
We perform all relevant imports and read in our primary dataset
#import
import pandas as pd
import numpy as np
import matplotlib.pyplot as plt
import seaborn as sns
import scipy.stats as stats
import folium
import geopandas as gpd
#make sure the csv is in your top level drive directory, if you try and put it in a subfolder then that filepath becomes invalid for the others
data = pd.read_csv('Housing.csv')
#data = pd.read_csv('/content/drive/My Drive/Housing.csv')
#data = pd.read_csv('/content/drive/My Drive/cmsc320-finalproject/Housing.csv')
Perform data cleaning and encoding of data types in incorrect/unusable formats
We also perform feature creation, it may be useful to have additional data such as the total number of rooms in a house and the price per square footage
data = pd.read_csv('Housing.csv')
#parse
#handling NaNs
print(data.isnull().sum())
data['bedrooms'] = data['bedrooms'].fillna(data['bedrooms'].median()) # Filling missing values
data['bathrooms'] = data['bathrooms'].fillna(data['bathrooms'].median())
data.dropna(subset=['price'], inplace=True) # Dropping rows where the 'price' is missing
data['yr_renovated'] = data['yr_renovated'].fillna(0) # Filling 'yr_renovated' with 0 where NaNs may imply no renovation
#string converts
data['date'] = pd.to_datetime(data['date'])
data['id'] = data['id'].astype(str)
#encoding
data['house_age'] = data['date'].dt.year - data['yr_built']
#should make years since renovation equal years since it was built if 0
#data['years_since_renovation'] = data.apply(lambda row: row['date'].year - row['yr_renovated'] if row['yr_renovated'] != 0 else 0, axis=1)
data['years_since_renovation'] = data.apply(
lambda row: row['date'].year - row['yr_renovated'] if row['yr_renovated'] != 0 else row['date'].year - row['yr_built'],
axis=1
)
#new cols
data['num_rooms'] = data['bedrooms'] + data['bathrooms']
data['living percentage'] = (data['sqft_living'])/(data['sqft_lot'])
data['price_per_sqft_living'] = data['price']/data['sqft_living']
data['price_per_sqft_lot'] = data['price']/data['sqft_lot']
id 0 date 0 price 0 bedrooms 0 bathrooms 0 sqft_living 0 sqft_lot 0 floors 0 waterfront 0 view 0 condition 0 grade 0 sqft_above 0 sqft_basement 0 yr_built 0 yr_renovated 0 zipcode 0 lat 0 long 0 sqft_living15 0 sqft_lot15 0 dtype: int64
# organize (sort by date)
data.sort_values(by='date', inplace=True)
data.reset_index(drop=True, inplace=True)
#general testing
data.head(10)
| id | date | price | bedrooms | bathrooms | sqft_living | sqft_lot | floors | waterfront | view | ... | lat | long | sqft_living15 | sqft_lot15 | house_age | years_since_renovation | num_rooms | living percentage | price_per_sqft_living | price_per_sqft_lot | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| 0 | 5561000190 | 2014-05-02 | 437500.0 | 3 | 2.25 | 1970 | 35100 | 2.0 | 0 | 0 | ... | 47.4635 | -121.991 | 2340 | 35100 | 37 | 37 | 5.25 | 0.056125 | 222.081218 | 12.464387 |
| 1 | 472000620 | 2014-05-02 | 790000.0 | 3 | 2.50 | 2600 | 4750 | 1.0 | 0 | 0 | ... | 47.6833 | -122.400 | 2380 | 4750 | 63 | 63 | 5.50 | 0.547368 | 303.846154 | 166.315789 |
| 2 | 1024069009 | 2014-05-02 | 675000.0 | 5 | 2.50 | 2820 | 67518 | 2.0 | 0 | 0 | ... | 47.5794 | -122.025 | 2820 | 48351 | 35 | 35 | 7.50 | 0.041767 | 239.361702 | 9.997334 |
| 3 | 7853361370 | 2014-05-02 | 555000.0 | 4 | 2.50 | 3310 | 6500 | 2.0 | 0 | 0 | ... | 47.5150 | -121.870 | 2380 | 5000 | 2 | 2 | 6.50 | 0.509231 | 167.673716 | 85.384615 |
| 4 | 5056500260 | 2014-05-02 | 440000.0 | 4 | 2.25 | 2160 | 8119 | 1.0 | 0 | 0 | ... | 47.5443 | -122.177 | 1850 | 9000 | 48 | 48 | 6.25 | 0.266043 | 203.703704 | 54.193866 |
| 5 | 3438501320 | 2014-05-02 | 295000.0 | 2 | 2.50 | 1630 | 1368 | 2.0 | 0 | 0 | ... | 47.5489 | -122.363 | 1590 | 2306 | 5 | 5 | 4.50 | 1.191520 | 180.981595 | 215.643275 |
| 6 | 1737320120 | 2014-05-02 | 470000.0 | 5 | 2.50 | 2210 | 9655 | 1.0 | 0 | 0 | ... | 47.7698 | -122.222 | 2080 | 8633 | 38 | 38 | 7.50 | 0.228897 | 212.669683 | 48.679441 |
| 7 | 7197300105 | 2014-05-02 | 550000.0 | 4 | 2.50 | 1940 | 10500 | 1.0 | 0 | 0 | ... | 47.6830 | -122.114 | 2200 | 10500 | 38 | 38 | 6.50 | 0.184762 | 283.505155 | 52.380952 |
| 8 | 1999700045 | 2014-05-02 | 313000.0 | 3 | 1.50 | 1340 | 7912 | 1.5 | 0 | 0 | ... | 47.7658 | -122.339 | 1480 | 7940 | 59 | 59 | 4.50 | 0.169363 | 233.582090 | 39.560162 |
| 9 | 1962200037 | 2014-05-02 | 626000.0 | 3 | 2.25 | 1750 | 1572 | 2.5 | 0 | 0 | ... | 47.6498 | -122.321 | 2410 | 3050 | 9 | 9 | 5.25 | 1.113232 | 357.714286 | 398.218830 |
10 rows × 27 columns
Mihir's Section
As we are looking to explore this data set it may be a good idea to get an idea of how all the variables are interrelated
#Mihir - Covariance matrix of all features
CovMatrix = data.cov()
#However correlation matrix will be more useful as it scales everything using standard deviations to between -1 to 1, makes it easier to compare between factors
CorrMatrix = data.corr(method = 'pearson')
#prints much better if you stick it in its own cell
data.cov()
| id | date | price | bedrooms | bathrooms | sqft_living | sqft_lot | floors | waterfront | view | ... | lat | long | sqft_living15 | sqft_lot15 | house_age | years_since_renovation | num_rooms | living percentage | price_per_sqft_living | price_per_sqft_lot | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| id | 8.274654e+18 | 1.566785e+23 | -1.770230e+13 | 3.316999e+06 | 1.142695e+07 | -3.238863e+10 | -1.574064e+13 | 2.877320e+07 | -6.772400e+05 | 2.555269e+07 | ... | -7.539282e+05 | 8.425348e+06 | -5.722532e+09 | -1.090153e+13 | -1.792808e+09 | -1.434415e+09 | 1.474395e+07 | 6.806534e+07 | -1.749445e+09 | 1.618107e+10 |
| date | 1.566785e+23 | 9.540109e+31 | -1.562305e+19 | -1.525486e+14 | -2.588457e+14 | -3.100206e+17 | 2.553979e+18 | -1.186211e+14 | 1.145477e+12 | -1.347551e+13 | ... | -4.446697e+13 | -9.655969e+12 | -2.109778e+17 | 6.842317e+17 | 3.999961e+15 | 7.098913e+15 | -4.113943e+14 | -1.267093e+13 | 4.081743e+16 | 7.885853e+15 |
| price | -1.770230e+13 | -1.562305e+19 | 1.347821e+11 | 1.053004e+05 | 1.484810e+05 | 2.367150e+08 | 1.363432e+09 | 5.090779e+04 | 8.460640e+03 | 1.117729e+05 | ... | 1.561740e+04 | 1.118099e+03 | 1.472961e+08 | 8.264560e+08 | -5.818276e+05 | -1.117816e+06 | 2.537814e+05 | 1.213879e+04 | 2.241334e+07 | 1.063007e+07 |
| bedrooms | 3.316999e+06 | -1.525486e+14 | 1.053004e+05 | 8.650956e-01 | 3.695787e-01 | 4.926377e+02 | 1.221762e+03 | 8.812733e-02 | -5.293190e-04 | 5.669500e-02 | ... | -1.148704e-03 | 1.696024e-02 | 2.496817e+02 | 7.429740e+02 | -4.217009e+00 | -4.439367e+00 | 1.234674e+00 | 6.658814e-03 | -2.109089e+01 | -5.451275e+00 |
| bathrooms | 1.142695e+07 | -2.588457e+14 | 1.484810e+05 | 3.695787e-01 | 5.931513e-01 | 5.338120e+02 | 2.798944e+03 | 2.082114e-01 | 4.247388e-03 | 1.108004e-01 | ... | 2.622344e-03 | 2.419130e-02 | 3.001611e+02 | 1.833182e+03 | -1.145691e+01 | -1.192709e+01 | 9.627300e-01 | 5.922581e-02 | -7.749677e+00 | 1.464115e+01 |
| sqft_living | -3.238863e+10 | -3.100206e+17 | 2.367150e+08 | 4.926377e+02 | 5.338120e+02 | 8.435337e+05 | 6.574684e+06 | 1.755404e+02 | 8.249461e+00 | 2.003143e+02 | ... | 6.685035e+00 | 3.107108e+01 | 4.761601e+05 | 4.596302e+06 | -8.592709e+03 | -9.107057e+03 | 1.026450e+03 | 1.904793e+01 | -9.331851e+03 | 1.947152e+03 |
| sqft_lot | -1.574064e+13 | 2.553979e+18 | 1.363432e+09 | 1.221762e+03 | 2.798944e+03 | 6.574684e+06 | 1.715659e+09 | -1.163286e+02 | 7.741867e+01 | 2.371393e+03 | ... | -4.917661e+02 | 1.338837e+03 | 4.105319e+06 | 8.126540e+08 | -6.447493e+04 | -6.302673e+04 | 4.020705e+03 | -2.811031e+03 | -1.541897e+05 | -8.039670e+05 |
| floors | 2.877320e+07 | -1.186211e+14 | 5.090779e+04 | 8.812733e-02 | 2.082114e-01 | 1.755404e+02 | -1.163286e+02 | 2.915880e-01 | 1.107146e-03 | 1.218394e-02 | ... | 3.712271e-03 | 9.537583e-03 | 1.035866e+02 | -1.661524e+02 | -7.766885e+00 | -7.867447e+00 | 2.963387e-01 | 8.078183e-02 | 2.280253e-01 | 2.428315e+01 |
| waterfront | -6.772400e+05 | 1.145477e+12 | 8.460640e+03 | -5.293190e-04 | 4.247388e-03 | 8.249461e+00 | 7.741867e+01 | 1.107146e-03 | 7.485226e-03 | 2.664300e-02 | ... | -1.711161e-04 | -5.106370e-04 | 5.127103e+00 | 7.252979e+01 | 6.631481e-02 | 1.169693e-03 | 3.718069e-03 | -6.941712e-04 | 1.839817e+00 | 2.490478e-01 |
| view | 2.555269e+07 | -1.347551e+13 | 1.117729e+05 | 5.669500e-02 | 1.108004e-01 | 2.003143e+02 | 2.371393e+03 | 1.218394e-02 | 2.664300e-02 | 5.872426e-01 | ... | 6.537452e-04 | -8.460837e-03 | 1.472943e+02 | 1.518526e+03 | 1.203386e+00 | 4.036811e-01 | 1.674954e-01 | -2.690266e-04 | 1.863367e+01 | 5.681183e+00 |
| condition | -4.452067e+07 | -3.226869e+14 | 8.686852e+03 | 1.725115e-02 | -6.263824e-02 | -3.511460e+01 | -2.414616e+02 | -9.268648e-02 | 9.375805e-04 | 2.293397e-02 | ... | -1.347221e-03 | -9.760027e-03 | -4.140089e+01 | -6.050935e+01 | 6.894440e+00 | 7.416206e+00 | -4.538708e-02 | -2.727252e-02 | 7.329965e+00 | -5.252303e+00 |
| grade | 2.748834e+07 | -4.582380e+14 | 2.880262e+05 | 3.902840e-01 | 6.020054e-01 | 8.234077e+02 | 5.531997e+03 | 2.908243e-01 | 8.417993e-03 | 2.263832e-01 | ... | 1.858155e-02 | 3.283811e-02 | 5.745907e+02 | 3.827254e+03 | -1.544911e+01 | -1.561983e+01 | 9.922894e-01 | 6.053961e-02 | 1.588124e+01 | 2.412967e+01 |
| sqft_above | -2.582941e+10 | -2.258601e+17 | 1.841011e+08 | 3.678642e+02 | 4.370876e+02 | 6.666978e+05 | 6.294462e+06 | 2.342603e+02 | 5.163720e+00 | 1.063870e+02 | ... | -9.368779e-02 | 4.009385e+01 | 4.153850e+05 | 4.387534e+06 | -1.032007e+04 | -1.040758e+04 | 8.049518e+02 | 1.154410e+01 | -8.076881e+03 | -3.563238e+02 |
| sqft_basement | -6.559226e+09 | -8.416047e+16 | 5.261393e+07 | 1.247734e+02 | 9.672443e+01 | 1.768358e+05 | 2.802218e+05 | -5.871985e+01 | 3.085741e+00 | 9.392727e+01 | ... | 6.778723e+00 | -9.022770e+00 | 6.077510e+04 | 2.087679e+05 | 1.727359e+03 | 1.300528e+03 | 2.214979e+02 | 7.503838e+00 | -1.254971e+03 | 2.303476e+03 |
| yr_built | 1.806430e+09 | -1.019331e+14 | 5.824414e+05 | 4.212745e+00 | 1.144733e+01 | 8.580238e+03 | 6.458085e+04 | 7.761250e+00 | -6.648330e-02 | -1.202897e+00 | ... | -6.028713e-01 | 1.693346e+00 | 6.567732e+03 | 5.690946e+04 | -8.627491e+02 | -7.698889e+02 | 1.566008e+01 | 2.202409e+00 | -9.371025e+02 | 3.442951e+02 |
| yr_renovated | -1.953565e+10 | -9.615773e+16 | 1.864482e+07 | 7.042583e+00 | 1.569654e+01 | 2.042442e+04 | 1.271708e+05 | 1.374814e+00 | 3.227949e+00 | 3.198718e+01 | ... | 1.636217e+00 | -3.867676e+00 | -7.357744e+02 | 8.613634e+04 | 2.648760e+03 | -1.908793e+03 | 2.273912e+01 | -3.664272e-01 | 4.663262e+03 | 1.399137e+03 |
| zipcode | -1.265349e+09 | 7.335453e+14 | -1.045028e+06 | -7.601869e+00 | -8.400840e+00 | -9.800232e+03 | -2.871637e+05 | -1.708121e+00 | 1.401912e-01 | 3.478060e+00 | ... | 1.979855e+00 | -4.250293e+00 | -1.023266e+04 | -2.150769e+05 | 5.451781e+02 | 4.942046e+02 | -1.600271e+01 | 2.555770e+00 | 1.016621e+03 | 1.115758e+03 |
| lat | -7.539282e+05 | -4.446697e+13 | 1.561740e+04 | -1.148704e-03 | 2.622344e-03 | 6.685035e+00 | -4.917661e+02 | 3.712271e-03 | -1.711161e-04 | 6.537452e-04 | ... | 1.919990e-02 | -2.644336e-03 | 4.640056e+00 | -3.269542e+02 | 6.009785e-01 | 5.391607e-01 | 1.473640e-03 | 6.138167e-03 | 7.198930e+00 | 3.791880e+00 |
| long | 8.425348e+06 | -9.655969e+12 | 1.118099e+03 | 1.696024e-02 | 2.419130e-02 | 3.107108e+01 | 1.338837e+03 | 9.537583e-03 | -5.106370e-04 | -8.460837e-03 | ... | -2.644336e-03 | 1.983262e-02 | 3.229692e+01 | 9.784167e+02 | -1.693329e+00 | -1.553609e+00 | 4.115154e-02 | -7.729806e-03 | -3.658430e+00 | -3.569414e+00 |
| sqft_living15 | -5.722532e+09 | -2.109778e+17 | 1.472961e+08 | 2.496817e+02 | 3.001611e+02 | 4.761601e+05 | 4.105319e+06 | 1.035866e+02 | 5.127103e+00 | 1.472943e+02 | ... | 4.640056e+00 | 3.229692e+01 | 4.697612e+05 | 3.428259e+06 | -6.574697e+03 | -6.415450e+03 | 5.498428e+02 | -7.755340e+00 | 2.908721e+03 | -2.867380e+03 |
| sqft_lot15 | -1.090153e+13 | 6.842317e+17 | 8.264560e+08 | 7.429740e+02 | 1.833182e+03 | 4.596302e+06 | 8.126540e+08 | -1.661524e+02 | 7.252979e+01 | 1.518526e+03 | ... | -3.269542e+02 | 9.784167e+02 | 3.428259e+06 | 7.455182e+08 | -5.691054e+04 | -5.523156e+04 | 2.576156e+03 | -2.034166e+03 | -1.728430e+05 | -5.873583e+05 |
| house_age | -1.792808e+09 | 3.999961e+15 | -5.818276e+05 | -4.217009e+00 | -1.145691e+01 | -8.592709e+03 | -6.447493e+04 | -7.766885e+00 | 6.631481e-02 | 1.203386e+00 | ... | 6.009785e-01 | -1.693329e+00 | -6.574697e+03 | -5.691054e+04 | 8.629196e+02 | 7.701938e+02 | -1.567392e+01 | -2.203452e+00 | 9.394453e+02 | -3.438461e+02 |
| years_since_renovation | -1.434415e+09 | 7.098913e+15 | -1.117816e+06 | -4.439367e+00 | -1.192709e+01 | -9.107057e+03 | -6.302673e+04 | -7.867447e+00 | 1.169693e-03 | 4.036811e-01 | ... | 5.391607e-01 | -1.553609e+00 | -6.415450e+03 | -5.523156e+04 | 7.701938e+02 | 8.302260e+02 | -1.636646e+01 | -2.294506e+00 | 7.924248e+02 | -4.208357e+02 |
| num_rooms | 1.474395e+07 | -4.113943e+14 | 2.537814e+05 | 1.234674e+00 | 9.627300e-01 | 1.026450e+03 | 4.020705e+03 | 2.963387e-01 | 3.718069e-03 | 1.674954e-01 | ... | 1.473640e-03 | 4.115154e-02 | 5.498428e+02 | 2.576156e+03 | -1.567392e+01 | -1.636646e+01 | 2.197404e+00 | 6.588463e-02 | -2.884057e+01 | 9.189874e+00 |
| living percentage | 6.806534e+07 | -1.267093e+13 | 1.213879e+04 | 6.658814e-03 | 5.922581e-02 | 1.904793e+01 | -2.811031e+03 | 8.078183e-02 | -6.941712e-04 | -2.690266e-04 | ... | 6.138167e-03 | -7.729806e-03 | -7.755340e+00 | -2.034166e+03 | -2.203452e+00 | -2.294506e+00 | 6.588463e-02 | 7.212734e-02 | 3.447523e+00 | 2.263822e+01 |
| price_per_sqft_living | -1.749445e+09 | 4.081743e+16 | 2.241334e+07 | -2.109089e+01 | -7.749677e+00 | -9.331851e+03 | -1.541897e+05 | 2.280253e-01 | 1.839817e+00 | 1.863367e+01 | ... | 7.198930e+00 | -3.658430e+00 | 2.908721e+03 | -1.728430e+05 | 9.394453e+02 | 7.924248e+02 | -2.884057e+01 | 3.447523e+00 | 1.211332e+04 | 4.663091e+03 |
| price_per_sqft_lot | 1.618107e+10 | 7.885853e+15 | 1.063007e+07 | -5.451275e+00 | 1.464115e+01 | 1.947152e+03 | -8.039670e+05 | 2.428315e+01 | 2.490478e-01 | 5.681183e+00 | ... | 3.791880e+00 | -3.569414e+00 | -2.867380e+03 | -5.873583e+05 | -3.438461e+02 | -4.208357e+02 | 9.189874e+00 | 2.263822e+01 | 4.663091e+03 | 8.846382e+03 |
27 rows × 27 columns
However the correlation matrix will be more useful as it scales everything using standard deviations to between -1 to 1, makes it easier to compare between factors
data.corr(method = 'pearson')
| id | date | price | bedrooms | bathrooms | sqft_living | sqft_lot | floors | waterfront | view | ... | lat | long | sqft_living15 | sqft_lot15 | house_age | years_since_renovation | num_rooms | living percentage | price_per_sqft_living | price_per_sqft_lot | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| id | 1.000000 | 0.005576 | -0.016762 | 0.001240 | 0.005158 | -0.012259 | -0.132109 | 0.018524 | -0.002721 | 0.011592 | ... | -0.001891 | 0.020798 | -0.002903 | -0.138798 | -0.021216 | -0.017306 | 0.003458 | 0.088105 | -0.005526 | 0.059807 |
| date | 0.005576 | 1.000000 | -0.004357 | -0.016792 | -0.034410 | -0.034559 | 0.006313 | -0.022491 | 0.001356 | -0.001800 | ... | -0.032856 | -0.007020 | -0.031515 | 0.002566 | 0.013941 | 0.025224 | -0.028414 | -0.004830 | 0.037970 | 0.008584 |
| price | -0.016762 | -0.004357 | 1.000000 | 0.308377 | 0.525136 | 0.702035 | 0.089661 | 0.256793 | 0.266370 | 0.397294 | ... | 0.307003 | 0.021626 | 0.585378 | 0.082447 | -0.053950 | -0.105671 | 0.466325 | 0.123115 | 0.554701 | 0.307848 |
| bedrooms | 0.001240 | -0.016792 | 0.308377 | 1.000000 | 0.515932 | 0.576693 | 0.031713 | 0.175466 | -0.006578 | 0.079543 | ... | -0.008913 | 0.129482 | 0.391666 | 0.029256 | -0.154343 | -0.165650 | 0.895500 | 0.026657 | -0.206030 | -0.062314 |
| bathrooms | 0.005158 | -0.034410 | 0.525136 | 0.515932 | 1.000000 | 0.754665 | 0.087740 | 0.500653 | 0.063744 | 0.187737 | ... | 0.024573 | 0.223042 | 0.568634 | 0.087175 | -0.506407 | -0.537469 | 0.843270 | 0.286338 | -0.091426 | 0.202120 |
| sqft_living | -0.012259 | -0.034559 | 0.702035 | 0.576693 | 0.754665 | 1.000000 | 0.172826 | 0.353949 | 0.103818 | 0.284611 | ... | 0.052529 | 0.240223 | 0.756420 | 0.183286 | -0.318488 | -0.344135 | 0.753931 | 0.077223 | -0.092318 | 0.022541 |
| sqft_lot | -0.132109 | 0.006313 | 0.089661 | 0.031713 | 0.087740 | 0.172826 | 1.000000 | -0.005201 | 0.021604 | 0.074710 | ... | -0.085683 | 0.229521 | 0.144608 | 0.718557 | -0.052990 | -0.052809 | 0.065483 | -0.252697 | -0.033823 | -0.206367 |
| floors | 0.018524 | -0.022491 | 0.256793 | 0.175466 | 0.500653 | 0.353949 | -0.005201 | 1.000000 | 0.023698 | 0.029444 | ... | 0.049614 | 0.125419 | 0.279885 | -0.011269 | -0.489640 | -0.505651 | 0.370210 | 0.557030 | 0.003837 | 0.478120 |
| waterfront | -0.002721 | 0.001356 | 0.266370 | -0.006578 | 0.063744 | 0.103818 | 0.021604 | 0.023698 | 1.000000 | 0.401857 | ... | -0.014274 | -0.041910 | 0.086463 | 0.030703 | 0.026093 | 0.000469 | 0.028991 | -0.029875 | 0.193215 | 0.030605 |
| view | 0.011592 | -0.001800 | 0.397294 | 0.079543 | 0.187737 | 0.284611 | 0.074710 | 0.029444 | 0.401857 | 1.000000 | ... | 0.006157 | -0.078400 | 0.280439 | 0.072575 | 0.053458 | 0.018282 | 0.147448 | -0.001307 | 0.220932 | 0.078822 |
| condition | -0.023784 | -0.050769 | 0.036361 | 0.028502 | -0.124982 | -0.058753 | -0.008958 | -0.263768 | 0.016653 | 0.045990 | ... | -0.014941 | -0.106500 | -0.092824 | -0.003406 | 0.360665 | 0.395525 | -0.047051 | -0.156051 | 0.102344 | -0.085814 |
| grade | 0.008130 | -0.039912 | 0.667434 | 0.356978 | 0.664983 | 0.762704 | 0.113621 | 0.458183 | 0.082775 | 0.251321 | ... | 0.114084 | 0.198372 | 0.713202 | 0.119248 | -0.447415 | -0.461180 | 0.569477 | 0.191771 | 0.122757 | 0.218253 |
| sqft_above | -0.010843 | -0.027924 | 0.605567 | 0.477614 | 0.685342 | 0.876597 | 0.183512 | 0.523885 | 0.072075 | 0.167649 | ... | -0.000816 | 0.343803 | 0.731870 | 0.194050 | -0.424248 | -0.436188 | 0.655748 | 0.051908 | -0.088620 | -0.004575 |
| sqft_basement | -0.005152 | -0.019469 | 0.323816 | 0.303112 | 0.283770 | 0.435043 | 0.015286 | -0.245705 | 0.080588 | 0.276947 | ... | 0.110538 | -0.144765 | 0.200355 | 0.017276 | 0.132865 | 0.101985 | 0.337620 | 0.063132 | -0.025764 | 0.055337 |
| yr_built | 0.021379 | -0.000355 | 0.054011 | 0.154198 | 0.506019 | 0.318049 | 0.053080 | 0.489319 | -0.026161 | -0.053440 | ... | -0.148122 | 0.409356 | 0.326229 | 0.070958 | -0.999873 | -0.909652 | 0.359654 | 0.279186 | -0.289869 | 0.124622 |
| yr_renovated | -0.016907 | -0.024509 | 0.126434 | 0.018850 | 0.050739 | 0.055363 | 0.007644 | 0.006338 | 0.092885 | 0.103917 | ... | 0.029398 | -0.068372 | -0.002673 | 0.007854 | 0.224480 | -0.164923 | 0.038189 | -0.003397 | 0.105482 | 0.037034 |
| zipcode | -0.008221 | 0.001404 | -0.053201 | -0.152754 | -0.203866 | -0.199430 | -0.129574 | -0.059121 | 0.030285 | 0.084827 | ... | 0.267048 | -0.564072 | -0.279033 | -0.147221 | 0.346864 | 0.320563 | -0.201764 | 0.177860 | 0.172637 | 0.221714 |
| lat | -0.001891 | -0.032856 | 0.307003 | -0.008913 | 0.024573 | 0.052529 | -0.085683 | 0.049614 | -0.014274 | 0.006157 | ... | 1.000000 | -0.135512 | 0.048858 | -0.086419 | 0.147647 | 0.135043 | 0.007174 | 0.164945 | 0.472049 | 0.290953 |
| long | 0.020798 | -0.007020 | 0.021626 | 0.129482 | 0.223042 | 0.240223 | 0.229521 | 0.125419 | -0.041910 | -0.078400 | ... | -0.135512 | 1.000000 | 0.334605 | 0.254451 | -0.409323 | -0.382872 | 0.197125 | -0.204375 | -0.236033 | -0.269478 |
| sqft_living15 | -0.002903 | -0.031515 | 0.585378 | 0.391666 | 0.568634 | 0.756420 | 0.144608 | 0.279885 | 0.086463 | 0.280439 | ... | 0.048858 | 0.334605 | 1.000000 | 0.183192 | -0.326552 | -0.324856 | 0.541184 | -0.042132 | 0.038560 | -0.044480 |
| sqft_lot15 | -0.138798 | 0.002566 | 0.082447 | 0.029256 | 0.087175 | 0.183286 | 0.718557 | -0.011269 | 0.030703 | 0.072575 | ... | -0.086419 | 0.254451 | 0.183192 | 1.000000 | -0.070954 | -0.070204 | 0.063648 | -0.277401 | -0.057516 | -0.228713 |
| house_age | -0.021216 | 0.013941 | -0.053950 | -0.154343 | -0.506407 | -0.318488 | -0.052990 | -0.489640 | 0.026093 | 0.053458 | ... | 0.147647 | -0.409323 | -0.326552 | -0.070954 | 1.000000 | 0.909948 | -0.359946 | -0.279298 | 0.290573 | -0.124450 |
| years_since_renovation | -0.017306 | 0.025224 | -0.105671 | -0.165650 | -0.537469 | -0.344135 | -0.052809 | -0.505651 | 0.000469 | 0.018282 | ... | 0.135043 | -0.382872 | -0.324856 | -0.070204 | 0.909948 | 1.000000 | -0.383179 | -0.296511 | 0.249878 | -0.155286 |
| num_rooms | 0.003458 | -0.028414 | 0.466325 | 0.895500 | 0.843270 | 0.753931 | 0.065483 | 0.370210 | 0.028991 | 0.147448 | ... | 0.007174 | 0.197125 | 0.541184 | 0.063648 | -0.359946 | -0.383179 | 1.000000 | 0.165493 | -0.176774 | 0.065913 |
| living percentage | 0.088105 | -0.004830 | 0.123115 | 0.026657 | 0.286338 | 0.077223 | -0.252697 | 0.557030 | -0.029875 | -0.001307 | ... | 0.164945 | -0.204375 | -0.042132 | -0.277401 | -0.279298 | -0.296511 | 0.165493 | 1.000000 | 0.116634 | 0.896209 |
| price_per_sqft_living | -0.005526 | 0.037970 | 0.554701 | -0.206030 | -0.091426 | -0.092318 | -0.033823 | 0.003837 | 0.193215 | 0.220932 | ... | 0.472049 | -0.236033 | 0.038560 | -0.057516 | 0.290573 | 0.249878 | -0.176774 | 0.116634 | 1.000000 | 0.450463 |
| price_per_sqft_lot | 0.059807 | 0.008584 | 0.307848 | -0.062314 | 0.202120 | 0.022541 | -0.206367 | 0.478120 | 0.030605 | 0.078822 | ... | 0.290953 | -0.269478 | -0.044480 | -0.228713 | -0.124450 | -0.155286 | 0.065913 | 0.896209 | 0.450463 | 1.000000 |
27 rows × 27 columns
As our ultimate goal is to predict the price of a house based on its feature, the most relevant column of this matrix is of the price
#correlations of price with all other current variables
print(CorrMatrix['price'])
id -0.016762 date -0.004357 price 1.000000 bedrooms 0.308377 bathrooms 0.525136 sqft_living 0.702035 sqft_lot 0.089661 floors 0.256793 waterfront 0.266370 view 0.397294 condition 0.036361 grade 0.667434 sqft_above 0.605567 sqft_basement 0.323816 yr_built 0.054011 yr_renovated 0.126434 zipcode -0.053201 lat 0.307003 long 0.021626 sqft_living15 0.585378 sqft_lot15 0.082447 house_age -0.053950 years_since_renovation -0.105671 num_rooms 0.466325 living percentage 0.123115 price_per_sqft_living 0.554701 price_per_sqft_lot 0.307848 Name: price, dtype: float64
As we can see the grading system that has been used by the realtors is quite good and is fairly correlated with price, another factor that is hugely correlated with price is square footage, which is why it may be better to explore price per square footage to gain insight into what nontrivial qualities affect the price of a house
print(CorrMatrix['price_per_sqft_living'])
id -0.005526 date 0.037970 price 0.554701 bedrooms -0.206030 bathrooms -0.091426 sqft_living -0.092318 sqft_lot -0.033823 floors 0.003837 waterfront 0.193215 view 0.220932 condition 0.102344 grade 0.122757 sqft_above -0.088620 sqft_basement -0.025764 yr_built -0.289869 yr_renovated 0.105482 zipcode 0.172637 lat 0.472049 long -0.236033 sqft_living15 0.038560 sqft_lot15 -0.057516 house_age 0.290573 years_since_renovation 0.249878 num_rooms -0.176774 living percentage 0.116634 price_per_sqft_living 1.000000 price_per_sqft_lot 0.450463 Name: price_per_sqft_living, dtype: float64
We can also find all other correlations that may be of interest by printing those above a certain R^2 value
#finding all other correlations that may be of interest
correlationThreshold = 0.3
checkedList = []
for row in CorrMatrix.index:
for col in CorrMatrix.columns:
if (not row in checkedList) and (not col in checkedList) and (row != col) and (CorrMatrix[row][col] > correlationThreshold or CorrMatrix[row][col] < -correlationThreshold):
print(row, col, CorrMatrix[row][col])
checkedList.append(row)
price bedrooms 0.3083769180156153 price bathrooms 0.5251363218554719 price sqft_living 0.7020346040056666 price view 0.39729352797680806 price grade 0.6674342691668146 price sqft_above 0.6055670405615354 price sqft_basement 0.3238155679576574 price lat 0.3070033728790943 price sqft_living15 0.5853783781780082 price num_rooms 0.4663250127585262 price price_per_sqft_living 0.5547008682090738 price price_per_sqft_lot 0.30784846349389644 bedrooms bathrooms 0.5159316152210395 bedrooms sqft_living 0.57669257587632 bedrooms grade 0.3569778987944419 bedrooms sqft_above 0.47761446504670363 bedrooms sqft_basement 0.30311202501453155 bedrooms sqft_living15 0.39166621103010474 bedrooms num_rooms 0.8954995511941201 bathrooms sqft_living 0.7546652789673763 bathrooms floors 0.5006531725878747 bathrooms grade 0.664982533878076 bathrooms sqft_above 0.6853424758761565 bathrooms yr_built 0.5060194382852586 bathrooms sqft_living15 0.5686342895782276 bathrooms house_age -0.5064069441397088 bathrooms years_since_renovation -0.537469341028698 bathrooms num_rooms 0.8432702460643129 sqft_living floors 0.35394929023671473 sqft_living grade 0.7627044764584723 sqft_living sqft_above 0.8765965986813177 sqft_living sqft_basement 0.4350429736698242 sqft_living yr_built 0.3180487689964427 sqft_living sqft_living15 0.7564202590172292 sqft_living house_age -0.31848847620130405 sqft_living years_since_renovation -0.3441348746046749 sqft_living num_rooms 0.7539307566069245 sqft_lot sqft_lot15 0.7185567524330329 floors grade 0.45818251367194757 floors sqft_above 0.5238847102851497 floors yr_built 0.48931942474365014 floors house_age -0.48963996546979405 floors years_since_renovation -0.505650922321103 floors num_rooms 0.37021041036533103 floors living percentage 0.5570303807316453 floors price_per_sqft_lot 0.4781204780795243 waterfront view 0.4018573506975677 condition yr_built -0.36141656224866653 condition house_age 0.3606652284795277 condition years_since_renovation 0.39552514408825024 grade sqft_above 0.7559229376236478 grade yr_built 0.4469632049266092 grade sqft_living15 0.7132020930151758 grade house_age -0.4474152409756253 grade years_since_renovation -0.46118017003453 grade num_rooms 0.5694767212967314 sqft_above yr_built 0.423898351663744 sqft_above long 0.3438030174605131 sqft_above sqft_living15 0.7318702923539874 sqft_above house_age -0.4242475329942809 sqft_above years_since_renovation -0.4361880253823974 sqft_above num_rooms 0.6557477942021749 sqft_basement num_rooms 0.337619598952765 yr_built zipcode -0.3468691778552612 yr_built long 0.4093562026388897 yr_built sqft_living15 0.3262288995957142 yr_built house_age -0.9998732929914715 yr_built years_since_renovation -0.9096524794041762 yr_built num_rooms 0.3596537193321721 zipcode long -0.564071606442267 zipcode house_age 0.34686352751305144 zipcode years_since_renovation 0.32056344232979844 lat price_per_sqft_living 0.47204862811027676 long sqft_living15 0.33460498382715503 long house_age -0.4093228953977021 long years_since_renovation -0.3828719068575162 sqft_living15 house_age -0.3265517538903627 sqft_living15 years_since_renovation -0.32485560112321155 sqft_living15 num_rooms 0.5411840225422982 house_age years_since_renovation 0.9099482701339621 house_age num_rooms -0.3599461100668001 years_since_renovation num_rooms -0.3831789177472444 living percentage price_per_sqft_lot 0.89620946404785 price_per_sqft_living price_per_sqft_lot 0.4504632365624928
This creates a heatmap of all the houses so we can visualize all areas of interest that will be covered by our dataset
houses_map = folium.Map(location=[data['lat'].mean(), data['long'].mean()], zoom_start=10)
for _, row in data.iterrows():
folium.Marker(
[row['lat'], row['long']]
).add_to(houses_map)
houses_map.save('AllHouseLocations.html')
from folium.plugins import HeatMap
houses_heatmap = folium.Map(location=[data['lat'].mean(), data['long'].mean()], zoom_start=10)
heat_data = data[['lat', 'long']].values.tolist()
HeatMap(heat_data).add_to(houses_heatmap)
houses_heatmap.save('AllHouseLocationsHeatmap.html')
houses_heatmap
As we can see we cover most of the Seattle area, but not Seattle itself
First, we calculate summary statistics for categorical features such as 'waterfront', 'view', 'condition', 'grade', and 'floors'. This helps us understand the distribution and typical values of these categorical variables.
# Analysis on boolean/categorical data (waterfront, view, condition, grade, floors)
def calculate_summary_statistics(data, column_name):
count = data[column_name].count() # Count non-null entries
mean = data[column_name].mean() # Mean
std = data[column_name].std() # Standard deviation
min_val = data[column_name].min() # Minimum value
q25 = data[column_name].quantile(0.25) # 25th percentile
median = data[column_name].median() # Median
q75 = data[column_name].quantile(0.75) # 75th percentile
max_val = data[column_name].max() # Maximum value
return {
"Count": count,
"Mean": mean,
"Standard Deviation": std,
"Min": min_val,
"25th Percentile": q25,
"50th Percentile (Median)": median,
"75th Percentile": q75,
"Max": max_val
}
columns_to_analyze = ['waterfront', 'view', 'condition', 'grade', 'floors']
# Calculating and displaying summary statistics for each column
summary_statistics = {}
for column in columns_to_analyze:
summary_statistics[column] = calculate_summary_statistics(data, column)
summary_statistics
{'waterfront': {'Count': 21613,
'Mean': 0.007541757275713691,
'Standard Deviation': 0.08651719772790183,
'Min': 0,
'25th Percentile': 0.0,
'50th Percentile (Median)': 0.0,
'75th Percentile': 0.0,
'Max': 1},
'view': {'Count': 21613,
'Mean': 0.23430342849211122,
'Standard Deviation': 0.7663175692736391,
'Min': 0,
'25th Percentile': 0.0,
'50th Percentile (Median)': 0.0,
'75th Percentile': 0.0,
'Max': 4},
'condition': {'Count': 21613,
'Mean': 3.4094295100171195,
'Standard Deviation': 0.6507430463662562,
'Min': 1,
'25th Percentile': 3.0,
'50th Percentile (Median)': 3.0,
'75th Percentile': 4.0,
'Max': 5},
'grade': {'Count': 21613,
'Mean': 7.656873178179799,
'Standard Deviation': 1.1754587569743047,
'Min': 1,
'25th Percentile': 7.0,
'50th Percentile (Median)': 7.0,
'75th Percentile': 8.0,
'Max': 13},
'floors': {'Count': 21613,
'Mean': 1.4943089807060566,
'Standard Deviation': 0.5399888951423845,
'Min': 1.0,
'25th Percentile': 1.0,
'50th Percentile (Median)': 1.5,
'75th Percentile': 2.0,
'Max': 3.5}}
Next, we perform Chi-square tests to examine the independence between pairs of categorical variables. This statistical test helps us understand if there are significant associations between different property characteristics.
# Chi-Square Test to waterfront and view, waterfront and condition, view and condition, condition and grade, grade and floors
from scipy.stats import chi2_contingency
def chi_square_test(data, var1, var2):
contingency_table = pd.crosstab(data[var1], data[var2])
chi2, p, dof, expected = chi2_contingency(contingency_table)
return chi2, p, dof, expected
# Pairs of variables to test
variable_pairs = [
('waterfront', 'view'),
('waterfront', 'condition'),
('view', 'condition'),
('condition', 'grade'),
('grade', 'floors')
]
# Performing Chi-Square Tests
chi_square_results = {}
for var1, var2 in variable_pairs:
chi2, p, dof, expected = chi_square_test(data, var1, var2)
chi_square_results[(var1, var2)] = {'chi2': chi2, 'p-value': p, 'dof': dof, 'expected': expected}
chi_square_results
# Interpretation:
# Waterfront vs. View: The p-value is 0.0, which is less than 0.05, indicating that there is a significant association between the waterfront status and the view rating.
# Waterfront vs. Condition: The p-value is 0.039, which is less than 0.05, indicating that there is a significant association between the waterfront status and the condition of the house.
# View vs. Condition: The p-value is extremely low (1.82e-08), indicating a significant association between the view rating and the condition of the house.
# Condition vs. Grade: The p-value is 0.0, which is less than 0.05, indicating a significant association between the condition of the house and its grade.
# Grade vs. Floors: The p-value is 0.0, which is less than 0.05, indicating a significant association between the grade of the house and the number of floors.
{('waterfront', 'view'): {'chi2': 7572.5563318397735,
'p-value': 0.0,
'dof': 4,
'expected': array([[1.93420187e+04, 3.29496137e+02, 9.55737288e+02, 5.06153704e+02,
3.16594179e+02],
[1.46981308e+02, 2.50386342e+00, 7.26271226e+00, 3.84629621e+00,
2.40582057e+00]])},
('waterfront', 'condition'): {'chi2': 10.074729585287205,
'p-value': 0.03918751144589182,
'dof': 4,
'expected': array([[2.97737473e+01, 1.70702818e+02, 1.39251816e+04, 5.63617036e+03,
1.68817147e+03],
[2.26252718e-01, 1.29718225e+00, 1.05818396e+02, 4.28296396e+01,
1.28285291e+01]])},
('view', 'condition'): {'chi2': 68.50224408217254,
'p-value': 1.822893843270391e-08,
'dof': 16,
'expected': array([[2.70517744e+01, 1.55096840e+02, 1.26521149e+04, 5.12090089e+03,
1.53383561e+03],
[4.60833757e-01, 2.64211354e+00, 2.15531948e+02, 8.72358303e+01,
2.61292740e+01],
[1.33669551e+00, 7.66372091e+00, 6.25172489e+02, 2.53036460e+02,
7.57906353e+01],
[7.07907278e-01, 4.05866839e+00, 3.31088234e+02, 1.34006848e+02,
4.01383427e+01],
[4.42789062e-01, 2.53865729e+00, 2.07092444e+02, 8.38199695e+01,
2.51061398e+01]])},
('condition', 'grade'): {'chi2': 2225.6248376517715,
'p-value': 0.0,
'dof': 44,
'expected': array([[1.38805349e-03, 4.16416046e-03, 4.02535511e-02, 3.35908944e-01,
2.82885301e+00, 1.24661084e+01, 8.42270856e+00, 3.62975987e+00,
1.57405265e+00, 5.53833341e-01, 1.24924814e-01, 1.80446953e-02],
[7.95817332e-03, 2.38745200e-02, 2.30787026e-01, 1.92587794e+00,
1.62187572e+01, 7.14723546e+01, 4.82901957e+01, 2.08106232e+01,
9.02456855e+00, 3.17531116e+00, 7.16235599e-01, 1.03456253e-01],
[6.49192616e-01, 1.94757785e+00, 1.88265859e+01, 1.57104613e+02,
1.32305455e+03, 5.83039888e+03, 3.93930079e+03, 1.69763869e+03,
7.36184426e+02, 2.59027854e+02, 5.84273354e+01, 8.43950400e+00],
[2.62758525e-01, 7.88275575e-01, 7.61999722e+00, 6.35875630e+01,
5.35501874e+02, 2.35983431e+03, 1.59441873e+03, 6.87113543e+02,
2.97968167e+02, 1.04840651e+02, 2.36482672e+01, 3.41586082e+00],
[7.87026327e-02, 2.36107898e-01, 2.28237635e+00, 1.90460371e+01,
1.60395965e+02, 7.06828344e+02, 4.77567575e+02, 2.05807384e+02,
8.92487855e+01, 3.14023504e+01, 7.08323694e+00, 1.02313422e+00]])},
('grade', 'floors'): {'chi2': 6505.2900602236405,
'p-value': 0.0,
'dof': 55,
'expected': array([[4.94147041e-01, 8.83727386e-02, 3.81298293e-01, 7.44922038e-03,
2.83625596e-02, 3.70147596e-04],
[1.48244112e+00, 2.65118216e-01, 1.14389488e+00, 2.23476611e-02,
8.50876787e-02, 1.11044279e-03],
[1.43302642e+01, 2.56280942e+00, 1.10576505e+01, 2.16027391e-01,
8.22514228e-01, 1.07342803e-02],
[1.19583584e+02, 2.13862027e+01, 9.22741868e+01, 1.80271133e+00,
6.86373942e+00, 8.95757183e-02],
[1.00707167e+03, 1.80103641e+02, 7.77085921e+02, 1.51815111e+01,
5.78028964e+01, 7.54360801e-01],
[4.43793458e+03, 7.93675566e+02, 3.42443997e+03, 6.69014482e+01,
2.54724148e+02, 3.32429556e+00],
[2.99848425e+03, 5.36245778e+02, 2.31371804e+03, 4.52018692e+01,
1.72104011e+02, 2.24605561e+00],
[1.29219451e+03, 2.31094712e+02, 9.97095035e+02, 1.94797113e+01,
7.41680933e+01, 9.67935964e-01],
[5.60362745e+02, 1.00214686e+02, 4.32392264e+02, 8.44741591e+00,
3.21631426e+01, 4.19747374e-01],
[1.97164669e+02, 3.52607227e+01, 1.52138019e+02, 2.97223893e+00,
1.13166613e+01, 1.47688891e-01],
[4.44732337e+01, 7.95354648e+00, 3.43168463e+01, 6.70429834e-01,
2.55263036e+00, 3.33132837e-02],
[6.42391153e+00, 1.14884560e+00, 4.95687781e+00, 9.68398649e-02,
3.68713274e-01, 4.81191875e-03]])}}
We conduct a t-test to determine if there is a significant difference in the prices of houses with basements versus those without.
# Susie - Test if the mean price of houses with a basement is significantly different from those without a basement
from scipy.stats import ttest_ind
# Split data based on houses with/without basement
with_basement = data[data['sqft_basement'] > 0]
without_basement = data[data['sqft_basement'] == 0]
# Performing a t-test
t_stat, p_val = ttest_ind(with_basement['price'], without_basement['price'])
print(f"T-statistic: {t_stat}, P-value: {p_val}")
# Visualization
plt.figure(figsize=(10, 6))
sns.boxplot(x='sqft_basement', y='price', data=data.assign(sqft_basement=data['sqft_basement']>0))
plt.title('Price Distribution With vs. Without Basement')
plt.xlabel('Has Basement')
plt.ylabel('Price')
plt.show()
T-statistic: 26.93602313477148, P-value: 3.266907478647668e-157
As realtors often like to say, housing is all about location, location, location. And with the data we have on zipcodes we can see if this is really true. We can also scrape data externally to see what confounders, if any predict why a zip code may have more or less expensive houses (average income in a zip code, certain zipcodes being near the waterfront, etc.)
Most expensive vs. least expensive zipcodes
zipcode_df = data.groupby('zipcode').agg(
avg_price=('price', 'mean'),
avg_price_per_sqft=('price_per_sqft_living', 'mean'),
avg_sqft_living = ('sqft_living', 'mean'),
avg_sqft_lot = ('sqft_lot', 'mean'),
avg_age = ('house_age','mean'),
total_houses=('zipcode', 'size')
).reset_index()
zipcode_df
| zipcode | avg_price | avg_price_per_sqft | avg_sqft_living | avg_sqft_lot | avg_age | total_houses | |
|---|---|---|---|---|---|---|---|
| 0 | 98001 | 2.808047e+05 | 151.387938 | 1900.856354 | 14937.450276 | 33.643646 | 362 |
| 1 | 98002 | 2.342840e+05 | 151.174091 | 1627.743719 | 7517.633166 | 46.562814 | 199 |
| 2 | 98003 | 2.941113e+05 | 157.113414 | 1928.882143 | 10603.096429 | 37.457143 | 280 |
| 3 | 98004 | 1.355927e+06 | 475.435611 | 2909.022082 | 13104.220820 | 42.867508 | 317 |
| 4 | 98005 | 8.101649e+05 | 314.929231 | 2656.803571 | 19928.785714 | 44.553571 | 168 |
| ... | ... | ... | ... | ... | ... | ... | ... |
| 65 | 98177 | 6.761854e+05 | 292.918745 | 2323.333333 | 11904.403922 | 53.447059 | 255 |
| 66 | 98178 | 3.106486e+05 | 189.202933 | 1729.351145 | 8309.122137 | 59.061069 | 262 |
| 67 | 98188 | 2.890783e+05 | 169.007306 | 1802.772059 | 10126.080882 | 48.882353 | 136 |
| 68 | 98198 | 3.028789e+05 | 178.428610 | 1745.360714 | 10525.978571 | 47.614286 | 280 |
| 69 | 98199 | 7.918208e+05 | 376.546345 | 2161.798107 | 5436.283912 | 57.798107 | 317 |
70 rows × 7 columns
plt.figure(figsize=(14, 8))
sns.boxplot(x='zipcode', y='price', data=data)
plt.xticks(rotation=90)
plt.title('Price Distribution by Zip Code')
plt.xlabel('Zip Code')
plt.ylabel('Price')
plt.show()
Let's see if there are any other variables we can check that may be spatially similar and may be confounding our analysis of the price in different zip codes, for example Average house age per zipcode.
zipcode_df["house_age"] = data.groupby("zipcode").apply(lambda x: x["house_age"].mean()).sort_values(ascending=False)
zipcode_df.corr(method="pearson")
| zipcode | avg_price | avg_price_per_sqft | avg_sqft_living | avg_sqft_lot | avg_age | total_houses | house_age | |
|---|---|---|---|---|---|---|---|---|
| zipcode | 1.000000 | -0.097518 | 0.151576 | -0.408197 | -0.348230 | 0.622144 | 0.024878 | NaN |
| avg_price | -0.097518 | 1.000000 | 0.865891 | 0.765753 | -0.077480 | 0.112726 | -0.150655 | NaN |
| avg_price_per_sqft | 0.151576 | 0.865891 | 1.000000 | 0.397018 | -0.214734 | 0.471106 | -0.078179 | NaN |
| avg_sqft_living | -0.408197 | 0.765753 | 0.397018 | 1.000000 | 0.186817 | -0.461699 | -0.092070 | NaN |
| avg_sqft_lot | -0.348230 | -0.077480 | -0.214734 | 0.186817 | 1.000000 | -0.364846 | -0.323261 | NaN |
| avg_age | 0.622144 | 0.112726 | 0.471106 | -0.461699 | -0.364846 | 1.000000 | -0.145524 | NaN |
| total_houses | 0.024878 | -0.150655 | -0.078179 | -0.092070 | -0.323261 | -0.145524 | 1.000000 | NaN |
| house_age | NaN | NaN | NaN | NaN | NaN | NaN | NaN | NaN |
However there doesn't appear to be any correlation between the average price per square foot and the age of house, which means it's not really relevant to our end analysis
However Zip codes are still a pretty good way of correlating our listings to other data of interest (employment, annual income, education, modes of transportation). We can use another data source to get this information and compare it to our existing data. https://www.uszipcodes.com has information for each zip code in an easy to parse format, so we can just scrape it for each zip code of interest.
This might be interesting: https://www.unitedstateszipcodes.org/98039/ We can scrape information off this for each zip code (only 70 so should be pretty easy) and do some cool stuff like look at preferred transportation, school enrollment or median salary
data["zipcode"].unique()
array([98027, 98117, 98029, 98065, 98006, 98106, 98011, 98052, 98133,
98102, 98001, 98092, 98125, 98059, 98199, 98115, 98107, 98024,
98155, 98072, 98042, 98116, 98034, 98119, 98077, 98045, 98105,
98007, 98074, 98166, 98008, 98198, 98003, 98014, 98136, 98023,
98033, 98038, 98103, 98055, 98075, 98058, 98122, 98053, 98118,
98112, 98004, 98177, 98019, 98144, 98056, 98005, 98168, 98146,
98028, 98108, 98040, 98148, 98010, 98030, 98178, 98032, 98109,
98126, 98031, 98070, 98022, 98188, 98002, 98039])
#data scraping
from bs4 import BeautifulSoup
import csv
import pandas as pd
import requests
import re
#needed to avoid 403 when scraping
headers = {
'Accept': 'text/html,application/xhtml+xml,application/xml;q=0.9,image/avif,image/webp,image/apng,*/*;q=0.8,application/signed-exchange;v=b3;q=0.7',
'Accept-Encoding': 'gzip, deflate, br, zstd',
'Accept-Language': 'en-US,en;q=0.9',
'Cache-Control': 'no-cache',
'Content-Type': 'application/x-www-form-urlencoded',
'Cookie': '_pk_id.29.e1c2=968bcc07b503e521.1718492157.; _li_dcdm_c=.unitedstateszipcodes.org; _lc2_fpi=16307b161960--01j0f1tnk55mz01jmc7j0n6f4e; _lc2_fpi_meta=%7B%22w%22%3A1718492157541%7D; cookie=648b908f-3427-4565-9b77-6d7d2cf00ee6; cookie_cst=zix7LPQsHA%3D%3D; _lr_env_src_ats=false; pbjs_fabrickId=%7B%22fabrickId%22%3A%22E1%3ABYenz68hhbaBPFJ1Oj_JfqhZdleyyEAv3MXzzDpE6CReGlkktJA3lH3MDFyhym_EWoRqQxCPIQwjZRGnabsXQNLHY1PUkXC4K3eblBLxttU%22%7D; pbjs_fabrickId_cst=zix7LPQsHA%3D%3D; ccuid=2d625ca7-9c69-4080-9aba-7609f84a642d; _au_1d=AU1D-0100-001718492158-GDMN4A82-A886; __qca=P0-2052112755-1718492157874; _gid=GA1.2.1291931010.1718492158; TAPAD=%7B%22id%22%3A%2240eada16-938c-4448-beaf-90cf62ce46dc%22%7D; _ga_FVWZ0RM4DH=GS1.1.1718554833.3.0.1718554833.60.0.0; _pk_ref.29.e1c2=%5B%22%22%2C%22%22%2C1718554834%2C%22https%3A%2F%2Fwww.google.com%2F%22%5D; _pk_ses.29.e1c2=1; _lr_retry_request=true; cto_bidid=cnESVV9RNkZPRFp3RDglMkJtbHk4bGFuVzZUQndic0l2ckNWciUyRk1iMWhIJTJCbHBoMUdyUDdLJTJGeXY4SW9OOTAxMmh3c2FxMWNUa2pad1lFRmhWc2RmT1Z1RTh4UXU0RDRkZ1Z3bkV0TXVTNGx3MkY4MEpIRktqYVZkaWxodVhUWThDTFRjMlZU; cto_bundle=7ktvOV9MciUyRmd1UGRPYm51bEolMkJIakxuT3VyYlZEdEFQR25WYktXc0s5ZUZxTGIlMkZnQ3llYmRIRTglMkYlMkJKVGpBMTFnMSUyRmdBekk0elp6ellUVzYzUUZzMkRIZnZ0a29GM09xanNrVGgxZnk2R3BqSjZQRSUyRmZ2NUp4d1UlMkJqME81Zzl4RHRyVHpjbThZNWh1RTNCciUyQkp0d2x0cFRnWk51WVkxc1RMemthckpucXBDaUxEUnclM0Q; _ga=GA1.2.1875332805.1718492158; __gads=ID=c3827d46571af6b6:T=1718492159:RT=1718554835:S=ALNI_MbF3JKPcwhXpg35XAKEgxes68-f9A; __gpi=UID=00000e2b1626d22d:T=1718492159:RT=1718554835:S=ALNI_MaaESawrsYVZVFcWJE30dFjsbQ2sg; __eoi=ID=7a68658352ef795b:T=1718492159:RT=1718554835:S=AA-AfjYDklsM5NxCrHNXmNd2hVS4; datadome=J~WQOWI5swjXmp~QZmI5Uf0JqgJNeb5sYpoyJyUEJYQBXs1_pYjlIB8S7jCfSUbJaCVNudVVr5IR1m9ThUYrZVduJ7ec1j7GjLWjz6R~qAwK0~zr2Lz1g0gQWk0RnYCX',
'Origin': 'https://www.unitedstateszipcodes.org',
'Pragma': 'no-cache',
'Priority': 'u=0,i',
'Referer': "https://www.unitedstateszipcodes.org/",
'Sec-Ch-Ua': '"Google Chrome";v="125", "Chromium";v="125", "Not.A/Brand";v="24"',
'Sec-Ch-Ua-Mobile': "?0",
'Sec-Ch-Ua-Platform': '"Windows"',
'Sec-Fetch-Dest': 'document',
'Sec-Fetch-Mode': 'navigate',
'Sec-Fetch-Site': 'same-origin',
'Sec-Fetch-User': '?1',
'Upgrade-Insecure-Requests': '1',
'User-Agent': "Mozilla/5.0 (Windows NT 10.0; Win64; x64) AppleWebKit/537.36 (KHTML, like Gecko) Chrome/125.0.0.0 Safari/537.36"
}
#much of the data is in tables;
#tags_of_interest contains the labeled data we care about
#when the tuple has two elements the first is the tag and the second is the label
#when the tuple has three elements, the third is the key for the dictionary
tags_of_interest = [("th", "Population"), ("th", "Population Density"), ("th", "Housing Units"), ("th", "Median Home Value"), ("th", "Land Area"), ("th", "Water Area"), ("th", "Occupied Housing Units"), ("th", "Median Household Income"),
("td", "Median Age: ", "Median Age"), ("td", "Male Median Age: ", "Male Median Age"), ("td", "Female Median Age: ", "Female Median Age"), ("th", 'Male', "Male Population"), ("th", "Female", "Female Population"), ("th", "White", "White Population"), ("th", "Black", "Black or African American Population"), ("th", "American Indian", "American Indian or Alaskan Native Population"), ("th", "Asian", "Asian Population"), ("th", "Hawaiian", "Native Hawaiian and Other Pacific Islander Population"), ("th", "Other Race", "Other Race Population"), ("th", "Two Or More Races", "Two or More Races Population"), ("th", "Husband Wife", "Husband and Wife Family Households"), ("th", "Single Guardian", "Single Guardian Households"), ("th", "Singles", "Singles Households"), ("th", "Singles With Roommate", "Singles with Roommate Households"), ("th", "Households without Kids"), ("th", "Households with Kids"), ("th", "In Occupied Housing Units"), ("th", "Correctional Facility", "Correctional Facilities"), ("th", "Juvenile Facilities"), ("th", "Nursing Facilities"), ("th", "Other Institutional"), ("th", "College Student Housing"), ("th", "Military Quarters"), ("th", "Other Noninstitutional"), ("th", "Owned Households With A Mortgage", "Owned House with Mortgage"), ("th", "Owned Households Free", "Owned House Entirely"), ("th", "Renter Occupied Households", "House Occupied by Renter"), ("th", "Households Vacant"), ("th", "Studio Apartment", "Rented Studio Apartment"), ("th", "1 Bedroom", "Rented 1 Bedroom"), ("th", "2 Bedroom", "Rented 2 Bedroom"), ("th", "3+ Bedroom", "Rented 3+ Bedroom"), ("th", "Worked Full-time"), ("th", "Worked Part-time"), ("th", "No Earnings"), ("th", "Car, truck, or van", "Commute in Car, Truck, or Van"), ("th", "Public transportation", "Commute in Public Transportation"), ("th", "Taxicab", "Commute in Taxicab"), ("th", "Motorcycle", "Commute in Motorcycle"), ("th", "Bicycle", "Commute in Bicycle, Walking, Other"), ("th", "Worked at Home"), ("th", "Less than High School Diploma"), ("th", "High School Graduate"), ("th", "Associate's degree"), ("th", "Master's degree"), ("th", "Professional school degree"), ("th", "Doctorate degree"), ("th", "Enrolled in Public School"), ("th", "Enrolled in Private School"), ("th", "Not Enrolled in School")]
#get_sibling_after gets the value of the sibling after the tag with label
def get_sibling_after(soup, tag, label):
#find_contains returns true if tag.text contains label
def find_contains(value):
return value.name == tag and label in value.text.replace('\xa0', '')
return soup.find(find_contains).find_next_sibling().text
zipcodes = [98027, 98117, 98029, 98065, 98006, 98106, 98011, 98052, 98133,
98102, 98001, 98092, 98125, 98059, 98199, 98115, 98107, 98024,
98155, 98072, 98042, 98116, 98034, 98119, 98077, 98045, 98105,
98007, 98074, 98166, 98008, 98198, 98003, 98014, 98136, 98023,
98033, 98038, 98103, 98055, 98075, 98058, 98122, 98053, 98118,
98112, 98004, 98177, 98019, 98144, 98056, 98005, 98168, 98146,
98028, 98108, 98040, 98148, 98010, 98030, 98178, 98032, 98109,
98126, 98031, 98070, 98022, 98188, 98002, 98039]
zipcode_data = []
for zipcode in zipcodes:
url = f"https://www.unitedstateszipcodes.org/{zipcode}/"
print(f"Now scraping: {zipcode}\nURL: {url}\n")
page = requests.get(url, headers=headers)
soup = BeautifulSoup(page.content, "html.parser")
zdata = {"zipcode": zipcode}
for tag in tags_of_interest:
key = tag[2] if len(tag) == 3 else tag[1]
zdata[key] = get_sibling_after(soup, tag[0], tag[1])
zipcode_data.append(zdata)
#print(zipcode_data)
scraped_df = pd.DataFrame(zipcode_data).set_index('zipcode')
print(scraped_df.head())
scraped_df.to_csv("zipcode_data.csv")
Now scraping: 98027
URL: https://www.unitedstateszipcodes.org/98027/
Now scraping: 98117
URL: https://www.unitedstateszipcodes.org/98117/
Now scraping: 98029
URL: https://www.unitedstateszipcodes.org/98029/
Now scraping: 98065
URL: https://www.unitedstateszipcodes.org/98065/
Now scraping: 98006
URL: https://www.unitedstateszipcodes.org/98006/
Now scraping: 98106
URL: https://www.unitedstateszipcodes.org/98106/
Now scraping: 98011
URL: https://www.unitedstateszipcodes.org/98011/
Now scraping: 98052
URL: https://www.unitedstateszipcodes.org/98052/
Now scraping: 98133
URL: https://www.unitedstateszipcodes.org/98133/
Now scraping: 98102
URL: https://www.unitedstateszipcodes.org/98102/
Now scraping: 98001
URL: https://www.unitedstateszipcodes.org/98001/
Now scraping: 98092
URL: https://www.unitedstateszipcodes.org/98092/
Now scraping: 98125
URL: https://www.unitedstateszipcodes.org/98125/
Now scraping: 98059
URL: https://www.unitedstateszipcodes.org/98059/
Now scraping: 98199
URL: https://www.unitedstateszipcodes.org/98199/
Now scraping: 98115
URL: https://www.unitedstateszipcodes.org/98115/
Now scraping: 98107
URL: https://www.unitedstateszipcodes.org/98107/
Now scraping: 98024
URL: https://www.unitedstateszipcodes.org/98024/
Now scraping: 98155
URL: https://www.unitedstateszipcodes.org/98155/
Now scraping: 98072
URL: https://www.unitedstateszipcodes.org/98072/
Now scraping: 98042
URL: https://www.unitedstateszipcodes.org/98042/
Now scraping: 98116
URL: https://www.unitedstateszipcodes.org/98116/
Now scraping: 98034
URL: https://www.unitedstateszipcodes.org/98034/
Now scraping: 98119
URL: https://www.unitedstateszipcodes.org/98119/
Now scraping: 98077
URL: https://www.unitedstateszipcodes.org/98077/
Now scraping: 98045
URL: https://www.unitedstateszipcodes.org/98045/
Now scraping: 98105
URL: https://www.unitedstateszipcodes.org/98105/
Now scraping: 98007
URL: https://www.unitedstateszipcodes.org/98007/
Now scraping: 98074
URL: https://www.unitedstateszipcodes.org/98074/
Now scraping: 98166
URL: https://www.unitedstateszipcodes.org/98166/
Now scraping: 98008
URL: https://www.unitedstateszipcodes.org/98008/
Now scraping: 98198
URL: https://www.unitedstateszipcodes.org/98198/
Now scraping: 98003
URL: https://www.unitedstateszipcodes.org/98003/
Now scraping: 98014
URL: https://www.unitedstateszipcodes.org/98014/
Now scraping: 98136
URL: https://www.unitedstateszipcodes.org/98136/
Now scraping: 98023
URL: https://www.unitedstateszipcodes.org/98023/
Now scraping: 98033
URL: https://www.unitedstateszipcodes.org/98033/
Now scraping: 98038
URL: https://www.unitedstateszipcodes.org/98038/
Now scraping: 98103
URL: https://www.unitedstateszipcodes.org/98103/
Now scraping: 98055
URL: https://www.unitedstateszipcodes.org/98055/
Now scraping: 98075
URL: https://www.unitedstateszipcodes.org/98075/
Now scraping: 98058
URL: https://www.unitedstateszipcodes.org/98058/
Now scraping: 98122
URL: https://www.unitedstateszipcodes.org/98122/
Now scraping: 98053
URL: https://www.unitedstateszipcodes.org/98053/
Now scraping: 98118
URL: https://www.unitedstateszipcodes.org/98118/
Now scraping: 98112
URL: https://www.unitedstateszipcodes.org/98112/
Now scraping: 98004
URL: https://www.unitedstateszipcodes.org/98004/
Now scraping: 98177
URL: https://www.unitedstateszipcodes.org/98177/
Now scraping: 98019
URL: https://www.unitedstateszipcodes.org/98019/
Now scraping: 98144
URL: https://www.unitedstateszipcodes.org/98144/
Now scraping: 98056
URL: https://www.unitedstateszipcodes.org/98056/
Now scraping: 98005
URL: https://www.unitedstateszipcodes.org/98005/
Now scraping: 98168
URL: https://www.unitedstateszipcodes.org/98168/
Now scraping: 98146
URL: https://www.unitedstateszipcodes.org/98146/
Now scraping: 98028
URL: https://www.unitedstateszipcodes.org/98028/
Now scraping: 98108
URL: https://www.unitedstateszipcodes.org/98108/
Now scraping: 98040
URL: https://www.unitedstateszipcodes.org/98040/
Now scraping: 98148
URL: https://www.unitedstateszipcodes.org/98148/
Now scraping: 98010
URL: https://www.unitedstateszipcodes.org/98010/
Now scraping: 98030
URL: https://www.unitedstateszipcodes.org/98030/
Now scraping: 98178
URL: https://www.unitedstateszipcodes.org/98178/
Now scraping: 98032
URL: https://www.unitedstateszipcodes.org/98032/
Now scraping: 98109
URL: https://www.unitedstateszipcodes.org/98109/
Now scraping: 98126
URL: https://www.unitedstateszipcodes.org/98126/
Now scraping: 98031
URL: https://www.unitedstateszipcodes.org/98031/
Now scraping: 98070
URL: https://www.unitedstateszipcodes.org/98070/
Now scraping: 98022
URL: https://www.unitedstateszipcodes.org/98022/
Now scraping: 98188
URL: https://www.unitedstateszipcodes.org/98188/
Now scraping: 98002
URL: https://www.unitedstateszipcodes.org/98002/
Now scraping: 98039
URL: https://www.unitedstateszipcodes.org/98039/
Population Population Density Housing Units Median Home Value \
zipcode
98027 26,141 469 11,248 $478,800
98117 31,365 7,953 14,213 $463,500
98029 24,348 2,719 10,222 $446,900
98065 12,699 171 4,556 $418,900
98006 36,364 3,402 13,891 $574,000
Land Area Water Area Occupied Housing Units Median Household Income \
zipcode
98027 55.79 1.13 10,454 $100,644
98117 3.94 0.61 13,667 $86,986
98029 8.95 0.02 9,656 $99,974
98065 74.09 0.87 4,278 $121,415
98006 10.69 0.75 13,288 $110,290
Median Age Male Median Age ... Worked at Home \
zipcode ...
98027 41 40 ... 900
98117 40 39 ... 1,363
98029 35 34 ... 841
98065 34 34 ... 451
98006 42 41 ... 1,368
Less than High School Diploma High School Graduate Associate's degree \
zipcode
98027 703 6,547 1,545
98117 646 5,998 1,627
98029 400 4,577 1,546
98065 234 2,747 655
98006 559 6,238 1,955
Master's degree Professional school degree Doctorate degree \
zipcode
98027 3,365 684 314
98117 4,072 1,290 606
98029 2,925 593 690
98065 1,063 313 90
98006 4,184 1,361 1,137
Enrolled in Public School Enrolled in Private School \
zipcode
98027 3,680 711
98117 2,831 1,458
98029 4,359 965
98065 2,397 908
98006 6,315 1,363
Not Enrolled in School
zipcode
98027 286
98117 292
98029 556
98065 213
98006 422
[5 rows x 60 columns]
Once we've scraped the data we'll save it
#comment out if csv doesn't exist yet
scraped_df = pd.read_csv('zipcode_data.csv')
scraped_zipcode_df = pd.merge(zipcode_df, scraped_df, on = 'zipcode', how='left').reset_index()
scraped_zipcode_df.head()
| index | zipcode | avg_price | avg_price_per_sqft | avg_sqft_living | avg_sqft_lot | avg_age | total_houses | house_age | Population | ... | Worked at Home | Less than High School Diploma | High School Graduate | Associate's degree | Master's degree | Professional school degree | Doctorate degree | Enrolled in Public School | Enrolled in Private School | Not Enrolled in School | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| 0 | 0 | 98001 | 2.808047e+05 | 151.387938 | 1900.856354 | 14937.450276 | 33.643646 | 362 | NaN | 31,911 | ... | 579 | 1,957 | 12,586 | 3,015 | 942 | 152 | 72 | 5,979 | 470 | 800 |
| 1 | 1 | 98002 | 2.342840e+05 | 151.174091 | 1627.743719 | 7517.633166 | 46.562814 | 199 | NaN | 31,647 | ... | 361 | 3,924 | 13,231 | 1,922 | 587 | 149 | 20 | 5,325 | 243 | 1,112 |
| 2 | 2 | 98003 | 2.941113e+05 | 157.113414 | 1928.882143 | 10603.096429 | 37.457143 | 280 | NaN | 44,151 | ... | 944 | 3,570 | 15,997 | 3,049 | 1,212 | 296 | 156 | 6,956 | 601 | 1,446 |
| 3 | 3 | 98004 | 1.355927e+06 | 475.435611 | 2909.022082 | 13104.220820 | 42.867508 | 317 | NaN | 27,946 | ... | 1,454 | 653 | 5,275 | 1,384 | 4,170 | 1,253 | 715 | 2,904 | 1,385 | 462 |
| 4 | 4 | 98005 | 8.101649e+05 | 314.929231 | 2656.803571 | 19928.785714 | 44.553571 | 168 | NaN | 17,714 | ... | 524 | 454 | 2,954 | 875 | 2,368 | 500 | 412 | 2,148 | 566 | 185 |
5 rows × 69 columns
Now we can create maps showing how each of these features from the original dataset and the ones we've scraped vary by zipcode, we do this through the use of folium and geopy. after obtaining the washington zipcodes geojson from OpenDataDE (https://github.com/OpenDataDE/State-zip-code-GeoJSON) we can use folium to plot these values by zipcodes as choropleth maps that we will save as html files
zipcodes_geojson = 'washington_zipcodes.geojson'
gdf = gpd.read_file(zipcodes_geojson)
import folium
gdf.to_csv('gdf.csv')
scraped_zipcode_df['Population'] = scraped_zipcode_df['Population'].str.replace(',', '').astype(int)
for column in scraped_zipcode_df.columns:
if scraped_zipcode_df[column].dtype != 'object':
scraped_zipcode_df[column].fillna(scraped_zipcode_df[column].mean(),inplace=True)
scraped_zipcode_df = scraped_zipcode_df.apply(pd.to_numeric, errors='coerce')
scraped_zipcode_df.dropna(axis=1, inplace=True)
html_files = []
for column in scraped_zipcode_df.columns:
if (column != 'zipcode' and column != 'index'):
print(column)
column_map = folium.Map(location=[47.6061, -122.3328], zoom_start=10)
folium.Choropleth(
geo_data=gdf,
name=f'choropleth_{column}',
data=scraped_zipcode_df,
columns=['zipcode', column],
key_on='feature.properties.ZCTA5CE10',
fill_color='YlOrRd',
fill_opacity=0.7,
line_opacity=0.2,
legend_name=f'{column}'
).add_to(column_map)
file_name = f'choropleth_{column}.html'
html_files.append(file_name)
column_map.save(file_name)
print(f'Saved {file_name}')
column_map
avg_price Saved choropleth_avg_price.html avg_price_per_sqft Saved choropleth_avg_price_per_sqft.html avg_sqft_living Saved choropleth_avg_sqft_living.html avg_sqft_lot Saved choropleth_avg_sqft_lot.html avg_age Saved choropleth_avg_age.html total_houses Saved choropleth_total_houses.html Population Saved choropleth_Population.html Land Area Saved choropleth_Land Area.html Water Area Saved choropleth_Water Area.html Median Age Saved choropleth_Median Age.html Male Median Age Saved choropleth_Male Median Age.html Female Median Age Saved choropleth_Female Median Age.html Correctional Facilities Saved choropleth_Correctional Facilities.html Juvenile Facilities Saved choropleth_Juvenile Facilities.html Nursing Facilities Saved choropleth_Nursing Facilities.html Other Institutional Saved choropleth_Other Institutional.html Military Quarters Saved choropleth_Military Quarters.html Other Noninstitutional Saved choropleth_Other Noninstitutional.html Commute in Taxicab Saved choropleth_Commute in Taxicab.html Commute in Motorcycle Saved choropleth_Commute in Motorcycle.html
We can display these html files in the colab, however you may have trouble viewing them as a submission, so it may be easier to simply open the saved html file created by this script saved in the folder of this project
from IPython.display import IFrame
for html_file in html_files:
print(html_file)
display(IFrame(html_file, width=700, height=500))
choropleth_avg_price.html
choropleth_avg_price_per_sqft.html
choropleth_avg_sqft_living.html
choropleth_avg_sqft_lot.html
choropleth_avg_age.html
choropleth_total_houses.html
choropleth_Population.html
choropleth_Land Area.html
choropleth_Water Area.html
choropleth_Median Age.html
choropleth_Male Median Age.html
choropleth_Female Median Age.html
choropleth_Correctional Facilities.html
choropleth_Juvenile Facilities.html
choropleth_Nursing Facilities.html
choropleth_Other Institutional.html
choropleth_Military Quarters.html
choropleth_Other Noninstitutional.html
choropleth_Commute in Taxicab.html
choropleth_Commute in Motorcycle.html
Using our zipcode dataframe, we will perform ANOVA to see if there is a significant difference between zipcodes on average house price and price per square foot. Later, when we need to prune the dataset for relevant features we'll be able to cross reference this against the correlation table and our scraped data to see which features of zipcodes most affect housing prices and prices per square foot
groups = [group['price'].values for name, group in data.groupby('zipcode')]
f_statistic, p_value = stats.f_oneway(*groups)
print(f"F-statistic: {f_statistic}, p-value: {p_value}")
F-statistic: 214.6322029409192, p-value: 0.0
groups = [group['price_per_sqft_living'].values for name, group in data.groupby('zipcode')]
f_statistic, p_value = stats.f_oneway(*groups)
print(f"F-statistic: {f_statistic}, p-value: {p_value}")
F-statistic: 385.57121676127895, p-value: 0.0
As can be seen the variance between zipcodes is extremely high, we can now perform post hoc testing using tukey's HSD
from statsmodels.stats.multicomp import pairwise_tukeyhsd
data_flat = np.concatenate(groups)
labels = []
for i, group in enumerate(groups):
labels.extend([f"Group{i+1}"] * len(group))
tukey_results = pairwise_tukeyhsd(data_flat, labels)
print(tukey_results)
/home/mihir/anaconda3/lib/python3.11/site-packages/scipy/integrate/_quadpack_py.py:1233: IntegrationWarning: The integral is probably divergent, or slowly convergent. quad_r = quad(f, low, high, args=args, full_output=self.full_output,
Multiple Comparison of Means - Tukey HSD, FWER=0.05 =========================================================== group1 group2 meandiff p-adj lower upper reject ----------------------------------------------------------- Group1 Group10 74.5993 0.0 47.4408 101.7578 True Group1 Group11 71.6966 0.0 39.8838 103.5094 True Group1 Group12 51.6138 0.0 24.2241 79.0035 True Group1 Group13 30.4185 0.0018 4.7731 56.0639 True Group1 Group14 -2.4681 1.0 -23.5761 18.6398 False Group1 Group15 103.8457 0.0 66.2659 141.4255 True Group1 Group16 100.1844 0.0 78.1593 122.2094 True Group1 Group17 73.7551 0.0 49.4957 98.0146 True Group1 Group18 120.6829 0.0 97.2432 144.1227 True Group1 Group19 3.7683 1.0 -21.1989 28.7354 False Group1 Group2 -0.2138 1.0 -27.1943 26.7666 False Group1 Group20 9.6525 1.0 -14.8296 34.1345 False Group1 Group21 2.8316 1.0 -28.8863 34.5495 False Group1 Group22 191.7745 0.0 169.9892 213.5598 True Group1 Group23 114.5643 0.0 93.8343 135.2944 True Group1 Group24 22.2683 0.0111 1.8562 42.6804 True Group1 Group25 416.6954 0.0 370.5681 462.8228 True Group1 Group26 235.9046 0.0 211.621 260.1882 True Group1 Group27 12.9605 0.9736 -7.7469 33.6679 False Group1 Group28 69.0766 0.0 42.977 95.1761 True Group1 Group29 128.9984 0.0 108.4784 149.5184 True Group1 Group3 5.7255 1.0 -18.6068 30.0578 False Group1 Group30 118.0839 0.0 95.97 140.1978 True Group1 Group31 29.0146 0.0022 4.377 53.6521 True Group1 Group32 64.1482 0.0 42.0472 86.2492 True Group1 Group33 26.8164 0.0005 5.2836 48.3492 True Group1 Group34 55.8544 0.0 34.4545 77.2543 True Group1 Group35 59.4981 0.0 35.839 83.1572 True Group1 Group36 129.9554 0.0 97.5458 162.3651 True Group1 Group37 96.1241 0.0 71.6165 120.6317 True Group1 Group38 114.2834 0.0 92.5997 135.9671 True Group1 Group39 117.2519 0.0 94.4792 140.0247 True Group1 Group4 324.0477 0.0 300.5297 347.5657 True Group1 Group40 92.8904 0.0 65.866 119.9148 True Group1 Group41 4.4263 1.0 -18.4764 27.329 False Group1 Group42 271.7846 0.0 237.8956 305.6736 True Group1 Group43 218.4531 0.0 198.1185 238.7877 True Group1 Group44 253.7664 0.0 227.9515 279.5814 True Group1 Group45 79.939 0.0 56.7603 103.1177 True Group1 Group46 231.564 0.0 206.8733 256.2548 True Group1 Group47 73.0553 0.0 45.4732 100.6375 True Group1 Group48 282.0133 0.0 248.6097 315.4168 True Group1 Group49 287.2499 0.0 262.6387 311.8612 True Group1 Group5 163.5413 0.0 134.9997 192.0829 True Group1 Group50 202.7563 0.0 182.2977 223.215 True Group1 Group51 197.163 0.0 173.8933 220.4327 True Group1 Group52 212.1476 0.0 191.4775 232.8177 True Group1 Group53 111.8676 0.0 90.8384 132.8968 True Group1 Group54 280.8691 0.0 253.188 308.5501 True Group1 Group55 216.1262 0.0 192.0316 240.2208 True Group1 Group56 131.0837 0.0 109.0336 153.1339 True Group1 Group57 141.4079 0.0 118.5546 164.2613 True Group1 Group58 102.5927 0.0 81.4399 123.7455 True Group1 Group59 185.8301 0.0 161.0583 210.6019 True Group1 Group6 147.7035 0.0 126.5867 168.8204 True Group1 Group60 160.8539 0.0 137.816 183.8918 True Group1 Group61 74.1035 0.0 49.9625 98.2445 True Group1 Group62 34.4441 0.5466 -9.1236 78.0118 False Group1 Group63 95.1311 0.0 73.5023 116.7599 True Group1 Group64 74.8092 0.0 49.7845 99.8339 True Group1 Group65 23.9846 0.073 -0.6266 48.5958 False Group1 Group66 141.5308 0.0 116.535 166.5266 True Group1 Group67 37.815 0.0 13.0159 62.6141 True Group1 Group68 17.6194 0.9958 -13.1303 48.369 False Group1 Group69 27.0407 0.0077 2.7084 51.373 True Group1 Group7 138.6611 0.0 108.3103 169.0118 True Group1 Group70 225.1584 0.0 201.6404 248.6764 True Group1 Group8 150.3298 0.0 126.0703 174.5893 True Group1 Group9 58.7074 0.0 24.1679 93.2469 True Group10 Group11 -2.9027 1.0 -38.0196 32.2142 False Group10 Group12 -22.9855 0.7428 -54.1518 8.1808 False Group10 Group13 -44.1808 0.0 -73.8259 -14.5357 True Group10 Group14 -77.0674 0.0 -102.8877 -51.2471 True Group10 Group15 29.2464 0.7879 -11.1687 69.6615 False Group10 Group16 25.5851 0.0863 -0.9902 52.1603 False Group10 Group17 -0.8442 1.0 -29.2988 27.6105 False Group10 Group18 46.0837 0.0 18.3246 73.8427 True Group10 Group19 -70.831 0.0 -99.8913 -41.7707 True Group10 Group2 -74.8131 0.0 -105.6204 -44.0059 True Group10 Group20 -64.9468 0.0 -93.5915 -36.3022 True Group10 Group21 -71.7677 0.0 -106.7987 -36.7368 True Group10 Group22 117.1752 0.0 90.7983 143.5521 True Group10 Group23 39.965 0.0 14.4527 65.4773 True Group10 Group24 -52.331 0.0 -77.5856 -27.0764 True Group10 Group25 342.0961 0.0 293.6309 390.5613 True Group10 Group26 161.3053 0.0 132.8301 189.7805 True Group10 Group27 -61.6388 0.0 -87.1327 -36.1449 True Group10 Group28 -5.5227 1.0 -35.5615 24.5161 False Group10 Group29 54.3991 0.0 29.0572 79.741 True Group10 Group3 -68.8738 0.0 -97.3905 -40.3571 True Group10 Group30 43.4846 0.0 16.8356 70.1335 True Group10 Group31 -45.5847 0.0 -74.3624 -16.8071 True Group10 Group32 -10.4511 1.0 -37.0894 16.1872 False Group10 Group33 -47.7829 0.0 -73.9516 -21.6141 True Group10 Group34 -18.7449 0.8012 -44.8044 7.3146 False Group10 Group35 -15.1012 0.999 -43.0457 12.8433 False Group10 Group36 55.3561 0.0 19.6976 91.0146 True Group10 Group37 21.5248 0.6961 -7.1416 50.1912 False Group10 Group38 39.6841 0.0 13.391 65.9772 True Group10 Group39 42.6526 0.0 15.4544 69.8508 True Group10 Group4 249.4484 0.0 221.6232 277.2735 True Group10 Group40 18.2911 0.9909 -12.5547 49.1369 False Group10 Group41 -70.173 0.0 -97.48 -42.866 True Group10 Group42 197.1853 0.0 160.1771 234.1935 True Group10 Group43 143.8538 0.0 118.6618 169.0458 True Group10 Group44 179.1671 0.0 149.3753 208.959 True Group10 Group45 5.3397 1.0 -22.1992 32.8787 False Group10 Group46 156.9647 0.0 128.1416 185.7879 True Group10 Group47 -1.5439 1.0 -32.8795 29.7916 False Group10 Group48 207.414 0.0 170.8498 243.9781 True Group10 Group49 212.6506 0.0 183.8955 241.4057 True Group10 Group5 88.942 0.0 56.7587 121.1253 True Group10 Group50 128.157 0.0 102.8648 153.4493 True Group10 Group51 122.5637 0.0 94.9481 150.1793 True Group10 Group52 137.5483 0.0 112.0847 163.0119 True Group10 Group53 37.2683 0.0 11.5123 63.0242 True Group10 Group54 206.2698 0.0 174.8471 237.6924 True Group10 Group55 141.5269 0.0 113.2128 169.8411 True Group10 Group56 56.4844 0.0 29.8883 83.0805 True Group10 Group57 66.8086 0.0 39.543 94.0743 True Group10 Group58 27.9934 0.0128 2.1364 53.8504 True Group10 Group59 111.2308 0.0 82.3382 140.1234 True Group10 Group6 73.1042 0.0 47.2767 98.9318 True Group10 Group60 86.2546 0.0 58.8341 113.6752 True Group10 Group61 -0.4958 1.0 -28.8495 27.8579 False Group10 Group62 -40.1552 0.265 -86.1909 5.8805 False Group10 Group63 20.5318 0.5787 -5.716 46.7796 False Group10 Group64 0.2099 1.0 -28.8998 29.3196 False Group10 Group65 -50.6147 0.0 -79.3698 -21.8596 True Group10 Group66 66.9315 0.0 37.8466 96.0164 True Group10 Group67 -36.7843 0.0003 -65.7004 -7.8682 True Group10 Group68 -56.9799 0.0 -91.1367 -22.8232 True Group10 Group69 -47.5586 0.0 -76.0754 -19.0419 True Group10 Group7 64.0618 0.0 30.2637 97.8599 True Group10 Group70 150.5591 0.0 122.734 178.3842 True Group10 Group8 75.7305 0.0 47.2759 104.1851 True Group10 Group9 -15.8919 1.0 -53.4966 21.7129 False Group11 Group12 -20.0828 0.9964 -55.3789 15.2133 False Group11 Group13 -41.2781 0.001 -75.2384 -7.3177 True Group11 Group14 -74.1647 0.0 -104.843 -43.4863 True Group11 Group15 32.1491 0.7478 -11.5299 75.8281 False Group11 Group16 28.4878 0.173 -2.8286 59.8042 False Group11 Group17 2.0586 1.0 -30.8677 34.9848 False Group11 Group18 48.9864 0.0 16.6593 81.3134 True Group11 Group19 -67.9283 0.0 -101.3794 -34.4772 True Group11 Group2 -71.9104 0.0 -106.8899 -36.931 True Group11 Group20 -62.0441 0.0 -95.1347 -28.9535 True Group11 Group21 -68.865 0.0 -107.616 -30.114 True Group11 Group22 120.0779 0.0 88.9297 151.2262 True Group11 Group23 42.8677 0.0 12.4482 73.2873 True Group11 Group24 -49.4283 0.0 -79.6321 -19.2245 True Group11 Group25 344.9988 0.0 293.7802 396.2175 True Group11 Group26 164.208 0.0 131.264 197.1521 True Group11 Group27 -58.7361 0.0 -89.1402 -28.3319 True Group11 Group28 -2.62 1.0 -36.9245 31.6846 False Group11 Group29 57.3018 0.0 27.025 87.5786 True Group11 Group3 -65.9711 0.0 -98.9511 -32.9911 True Group11 Group30 46.3873 0.0 15.0083 77.7663 True Group11 Group31 -42.682 0.0002 -75.8878 -9.4762 True Group11 Group32 -7.5484 1.0 -38.9183 23.8215 False Group11 Group33 -44.8801 0.0 -75.8523 -13.908 True Group11 Group34 -15.8422 0.9998 -46.7221 15.0378 False Group11 Group35 -12.1985 1.0 -44.6849 20.288 False Group11 Group36 58.2589 0.0 18.9396 97.5781 True Group11 Group37 24.4275 0.7419 -8.682 57.537 False Group11 Group38 42.5868 0.0 11.5095 73.6641 True Group11 Group39 45.5553 0.0 13.7086 77.4021 True Group11 Group4 252.3511 0.0 219.9673 284.7349 True Group11 Group40 21.1938 0.9861 -13.8195 56.2072 False Group11 Group41 -67.2703 0.0 -99.21 -35.3305 True Group11 Group42 200.088 0.0 159.5407 240.6352 True Group11 Group43 146.7565 0.0 116.605 176.908 True Group11 Group44 182.0699 0.0 147.9813 216.1584 True Group11 Group45 8.2424 1.0 -23.8958 40.3807 False Group11 Group46 159.8675 0.0 126.6222 193.1127 True Group11 Group47 1.3588 1.0 -34.0869 36.8044 False Group11 Group48 210.3167 0.0 170.1743 250.4591 True Group11 Group49 215.5534 0.0 182.3671 248.7396 True Group11 Group5 91.8447 0.0 55.6475 128.0419 True Group11 Group50 131.0597 0.0 100.8245 161.295 True Group11 Group51 125.4665 0.0 93.2625 157.6704 True Group11 Group52 140.451 0.0 110.0723 170.8298 True Group11 Group53 40.171 0.0001 9.5468 70.7952 True Group11 Group54 209.1725 0.0 173.6499 244.6951 True Group11 Group55 144.4297 0.0 111.6247 177.2346 True Group11 Group56 59.3872 0.0 28.0531 90.7212 True Group11 Group57 69.7114 0.0 37.807 101.6158 True Group11 Group58 30.8961 0.0455 0.1869 61.6054 True Group11 Group59 114.1335 0.0 80.828 147.439 True Group11 Group6 76.007 0.0 45.3225 106.6915 True Group11 Group60 89.1573 0.0 57.1205 121.1942 True Group11 Group61 2.4069 1.0 -30.4321 35.246 False Group11 Group62 -37.2524 0.6575 -86.1785 11.6736 False Group11 Group63 23.4345 0.6811 -7.6045 54.4736 False Group11 Group64 3.1126 1.0 -30.3814 36.6066 False Group11 Group65 -47.712 0.0 -80.8983 -14.5257 True Group11 Group66 69.8342 0.0 36.3618 103.3067 True Group11 Group67 -33.8816 0.0386 -67.2074 -0.5557 True Group11 Group68 -54.0772 0.0 -92.0398 -16.1146 True Group11 Group69 -44.6559 0.0 -77.6359 -11.6759 True Group11 Group7 66.9645 0.0 29.3243 104.6047 True Group11 Group70 153.4618 0.0 121.078 185.8456 True Group11 Group8 78.6332 0.0 45.707 111.5595 True Group11 Group9 -12.9892 1.0 -54.0816 28.1033 False Group12 Group13 -21.1953 0.8285 -51.0524 8.6618 False Group12 Group14 -54.0819 0.0 -80.1453 -28.0185 True Group12 Group15 52.2319 0.0002 11.661 92.8028 True Group12 Group16 48.5706 0.0 21.759 75.3821 True Group12 Group17 22.1414 0.6172 -6.5341 50.8168 False Group12 Group18 69.0692 0.0 41.0838 97.0545 True Group12 Group19 -47.8455 0.0 -77.1221 -18.569 True Group12 Group2 -51.8276 0.0 -82.839 -20.8163 True Group12 Group20 -41.9613 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As we can see there's significant variance between zipcodes, and having a look at the different heatmaps we can see that there's a variety of correlations between more expensive and less expensive zipcodes and other factors. For example there are the obvious ones such as median household income being correlated directly with avg home price in a zipcode but there are also less obvious ones such as more expensive zipcodes (in terms of price per sqft) having higher median ages.
Avg Price per sqft
Median Age
There are many more conclusions we can draw from this analysis, however suffice to say that we can confidently reject the null hypothesis and conclude that zipcodes significantly predict house price as a complex function of various other confounding variables that are also tied to zipcode
Next we can see whether the timing of the listing has any effect on the price, we can hypothesize that as the housing market changes this will affect the number, quality and price of the listings that are put up.
data.insert(2, 'Season', "")
def seasonCalc(x):
winter = [12, 1, 2]
spring = [3, 4, 5]
summer = [6, 7, 8]
fall = [9, 10, 11]
month = x.month
if(month in winter):
return "Winter"
if(month in spring):
return "Spring"
if(month in summer):
return "Summer"
if(month in fall):
return "Fall"
data['Season'] = data['date'].apply(lambda x: seasonCalc(x))
print(data['Season'].value_counts())
Season Spring 6520 Summer 6331 Fall 5063 Winter 3699 Name: count, dtype: int64
We will perform a Chi-Square Goodness of Fit Analysis on distribution of House Sales for the various seasons.
We must make sure that all requirements to perform the GoF test are met:
1) As we are looking at number sales in each season we have a single categorical variable.
2) As one house sale doesn't impact another house sale we have independence of observations.
3) The data is mutually exclusive since a house can only be sold in a single season.
4) There are atleast 5 house sales in each season.
$H_{0}$: The distribution of house sales across the 4 seasons is not uniformly distributed.
$H_{A}$: The distribution of house sales across the 4 seasons is not uniformly distributed.
observed_data = data['Season'].value_counts()
expected_data = pd.Series([len(data['Season'])/4] * 4)
_ , p_val = stats.chisquare(observed_data, expected_data)
print(p_val)
2.004746007881965e-205
As p is less than the alpha value of 0.05, we proceed to reject the Null Hypothesis. This means that the distribution of house sales across the 4 seasons is not uniformly distributed.
However, Looking at the data over time there appears to be uniformity indicating no substantial change in price over time.
Based on this visualization we see that the price data is relatively uniform with the price per square foot being between USD 500 and USD 800. This could potentialy be attributed due to some houses having better location and amenities in turn increasing the valuation.
plt.plot(data['date'], data['price'])
plt.title('Price of Houses over Time')
plt.xlabel('Date')
plt.ylabel('Price ($ Millions of USD)')
Text(0, 0.5, 'Price ($ Millions of USD)')
This data suggests that most houses are priced between USD 500,000 and USD 1,500,000 with the ocassional outlier of a USD 3,000,000+ house.
Now that we know what columns are relevant to predicting price we can see how an ML model performs using all the data available vs only the columns that we have determined are relevant through testing
#Using complete original data
from sklearn.model_selection import train_test_split
Y = data['price']
X = data.drop(['id', 'date', 'price', 'price_per_sqft_living', 'price_per_sqft_lot'], axis=1)
random_state = 42
#As we can't take date we will instead one hot encode the seasons
X['Summer'] = X['Season'].apply(lambda x: 1 if x == 'Summer' else 0)
X['Fall'] = X['Season'].apply(lambda x: 1 if x == 'Fall' else 0)
X['Winter'] = X['Season'].apply(lambda x: 1 if x == 'Winter' else 0)
X['Spring'] = X['Season'].apply(lambda x: 1 if x == 'Spring' else 0)
X = X.drop(['Season'], axis=1)
X_train, X_test, Y_train, Y_test = train_test_split(X, Y, random_state = random_state, shuffle = True)
print(X_train.columns)
Index(['bedrooms', 'bathrooms', 'sqft_living', 'sqft_lot', 'floors',
'waterfront', 'view', 'condition', 'grade', 'sqft_above',
'sqft_basement', 'yr_built', 'yr_renovated', 'zipcode', 'lat', 'long',
'sqft_living15', 'sqft_lot15', 'house_age', 'years_since_renovation',
'num_rooms', 'living percentage', 'Summer', 'Fall', 'Winter', 'Spring'],
dtype='object')
import torch
import torch.nn as nn
import torch.optim as optim
from sklearn.preprocessing import StandardScaler
import time
device = (
"cuda"
if torch.cuda.is_available()
else "mps"
if torch.backends.mps.is_available()
else "cpu"
)
#Converting to numpy arrays
X_train = X_train.values
X_test = X_test.values
Y_train = Y_train.values
Y_test = Y_test.values
#Normalizing features
scaler = StandardScaler()
X_train = scaler.fit_transform(X_train)
X_test = scaler.transform(X_test)
#Converting to PyTorch tensors
X_train = torch.tensor(X_train, dtype=torch.float32).to(device)
X_test = torch.tensor(X_test, dtype=torch.float32).to(device)
Y_train = torch.tensor(Y_train, dtype=torch.float32).view(-1, 1).to(device)
Y_test = torch.tensor(Y_test, dtype=torch.float32).view(-1, 1).to(device)
start_time = time.time()
class HousePricePredictor(nn.Module):
def __init__(self, input_size):
super(HousePricePredictor, self).__init__()
self.fc0 = nn.Linear(input_size, 512)
self.fc1 = nn.Linear(512, 256)
self.fc2 = nn.Linear(256, 128)
self.fc3 = nn.Linear(128, 64)
self.fc4 = nn.Linear(64, 1)
def forward(self, x):
x = torch.relu(self.fc0(x))
x = torch.relu(self.fc1(x))
x = torch.relu(self.fc2(x))
x = torch.relu(self.fc3(x))
x = self.fc4(x)
return x
input_size = X_train.shape[1]
model = HousePricePredictor(input_size).to(device)
#training loop
criterion = nn.MSELoss()
optimizer = optim.Adam(model.parameters(), lr=0.001)
train_losses = []
num_epochs = 10000
for epoch in range(num_epochs):
model.train()
optimizer.zero_grad()
outputs = model(X_train)
loss = criterion(outputs, Y_train)
loss.backward()
optimizer.step()
train_losses.append(loss.item())
if (epoch+1) % 10 == 0:
print(f'Epoch [{epoch+1}/{num_epochs}], Loss: {loss.item():.4f}')
#Evaluating the model
model.eval()
with torch.no_grad():
predictions = model(X_test)
test_loss = criterion(predictions, Y_test)
print(f'Test Loss: {test_loss.item():.4f}')
end_time = time.time()
training_time = end_time - start_time
print(f"Training time: {training_time:.2f} seconds")
plt.plot(range(num_epochs), train_losses, label='Training Losses')
plt.xlabel('Epoch')
plt.ylabel('Loss')
plt.title('Training Loss Curve')
plt.legend()
plt.show()
Epoch [10/10000], Loss: 433123917824.0000 Epoch [20/10000], Loss: 433086398464.0000 Epoch [30/10000], Loss: 432900997120.0000 Epoch [40/10000], Loss: 432219324416.0000 Epoch [50/10000], Loss: 430147371008.0000 Epoch [60/10000], Loss: 424738095104.0000 Epoch [70/10000], Loss: 412279668736.0000 Epoch [80/10000], Loss: 386660925440.0000 Epoch [90/10000], Loss: 339749470208.0000 Epoch [100/10000], Loss: 265112322048.0000 Epoch [110/10000], Loss: 169517957120.0000 Epoch [120/10000], Loss: 91106967552.0000 Epoch [130/10000], Loss: 72370700288.0000 Epoch [140/10000], Loss: 65880739840.0000 Epoch [150/10000], Loss: 58765479936.0000 Epoch [160/10000], Loss: 55995146240.0000 Epoch [170/10000], Loss: 53035900928.0000 Epoch [180/10000], Loss: 50626605056.0000 Epoch [190/10000], Loss: 48462565376.0000 Epoch [200/10000], Loss: 46523518976.0000 Epoch [210/10000], Loss: 44782870528.0000 Epoch [220/10000], Loss: 43214204928.0000 Epoch [230/10000], Loss: 41808957440.0000 Epoch [240/10000], Loss: 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#Trimming it down to what we know is relevant
Y = data['price']
X = data.drop(['id', 'date', 'price','condition', 'yr_built', 'yr_renovated', 'lat', 'long','house_age','living percentage','price_per_sqft_living', 'price_per_sqft_lot', 'years_since_renovation', 'sqft_living15', 'sqft_lot15', 'sqft_lot', 'Season'], axis=1)
random_state = 42
X_train, X_test, Y_train, Y_test = train_test_split(X, Y, random_state = random_state, shuffle = True)
print(X_train.columns)
Index(['bedrooms', 'bathrooms', 'sqft_living', 'floors', 'waterfront', 'view',
'grade', 'sqft_above', 'sqft_basement', 'zipcode', 'num_rooms'],
dtype='object')
#Converting to numpy arrays
X_train = X_train.values
X_test = X_test.values
Y_train = Y_train.values
Y_test = Y_test.values
#Normalizing features
scaler = StandardScaler()
X_train = scaler.fit_transform(X_train)
X_test = scaler.transform(X_test)
#Converting to PyTorch tensors
X_train = torch.tensor(X_train, dtype=torch.float32).to(device)
X_test = torch.tensor(X_test, dtype=torch.float32).to(device)
Y_train = torch.tensor(Y_train, dtype=torch.float32).view(-1, 1).to(device)
Y_test = torch.tensor(Y_test, dtype=torch.float32).view(-1, 1).to(device)
start_time = time.time()
class HousePricePredictor(nn.Module):
def __init__(self, input_size):
super(HousePricePredictor, self).__init__()
self.fc0 = nn.Linear(input_size, 512)
self.fc1 = nn.Linear(512, 256)
self.fc2 = nn.Linear(256, 128)
self.fc3 = nn.Linear(128, 64)
self.fc4 = nn.Linear(64, 1)
def forward(self, x):
x = torch.relu(self.fc0(x))
x = torch.relu(self.fc1(x))
x = torch.relu(self.fc2(x))
x = torch.relu(self.fc3(x))
x = self.fc4(x)
return x
input_size = X_train.shape[1]
model = HousePricePredictor(input_size).to(device)
#training loop
criterion = nn.MSELoss()
optimizer = optim.Adam(model.parameters(), lr=0.001)
train_losses = []
num_epochs = 10000
for epoch in range(num_epochs):
model.train()
optimizer.zero_grad()
outputs = model(X_train)
loss = criterion(outputs, Y_train)
loss.backward()
optimizer.step()
train_losses.append(loss.item())
if (epoch+1) % 10 == 0:
print(f'Epoch [{epoch+1}/{num_epochs}], Loss: {loss.item():.4f}')
#Evaluating the model
model.eval()
with torch.no_grad():
predictions = model(X_test)
test_loss = criterion(predictions, Y_test)
print(f'Test Loss: {test_loss.item():.4f}')
end_time = time.time()
training_time = end_time - start_time
print(f"Training time: {training_time:.2f} seconds")
plt.plot(range(num_epochs), train_losses, label='Training Losses')
plt.xlabel('Epoch')
plt.ylabel('Loss')
plt.title('Training Loss Curve')
plt.legend()
plt.show()
Epoch [10/10000], Loss: 433123753984.0000 Epoch [20/10000], Loss: 433085906944.0000 Epoch [30/10000], Loss: 432908173312.0000 Epoch [40/10000], Loss: 432290594816.0000 Epoch [50/10000], Loss: 430519877632.0000 Epoch [60/10000], Loss: 426108354560.0000 Epoch [70/10000], Loss: 416304168960.0000 Epoch [80/10000], Loss: 396611158016.0000 Epoch [90/10000], Loss: 360817459200.0000 Epoch [100/10000], Loss: 302777106432.0000 Epoch [110/10000], Loss: 222353539072.0000 Epoch [120/10000], Loss: 137843884032.0000 Epoch [130/10000], Loss: 92328861696.0000 Epoch [140/10000], Loss: 91405885440.0000 Epoch [150/10000], Loss: 85511929856.0000 Epoch [160/10000], Loss: 81505902592.0000 Epoch [170/10000], Loss: 78983544832.0000 Epoch [180/10000], Loss: 76222545920.0000 Epoch [190/10000], Loss: 73866297344.0000 Epoch [200/10000], Loss: 71644569600.0000 Epoch [210/10000], Loss: 69584281600.0000 Epoch [220/10000], Loss: 67693244416.0000 Epoch [230/10000], Loss: 65963782144.0000 Epoch [240/10000], Loss: 64397950976.0000 Epoch [250/10000], Loss: 62984855552.0000 Epoch [260/10000], Loss: 61716807680.0000 Epoch [270/10000], Loss: 60585517056.0000 Epoch [280/10000], Loss: 59581640704.0000 Epoch [290/10000], Loss: 58691244032.0000 Epoch [300/10000], Loss: 57902153728.0000 Epoch [310/10000], Loss: 57202495488.0000 Epoch [320/10000], Loss: 56581398528.0000 Epoch [330/10000], Loss: 56030064640.0000 Epoch [340/10000], Loss: 55539490816.0000 Epoch [350/10000], Loss: 55101911040.0000 Epoch [360/10000], Loss: 54709227520.0000 Epoch [370/10000], Loss: 54354247680.0000 Epoch [380/10000], Loss: 54032269312.0000 Epoch [390/10000], Loss: 53738221568.0000 Epoch [400/10000], Loss: 53469122560.0000 Epoch [410/10000], Loss: 53221863424.0000 Epoch [420/10000], Loss: 52992192512.0000 Epoch [430/10000], Loss: 52778631168.0000 Epoch [440/10000], Loss: 52579926016.0000 Epoch [450/10000], Loss: 52393545728.0000 Epoch [460/10000], Loss: 52218216448.0000 Epoch [470/10000], Loss: 52053381120.0000 Epoch 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As can be seen we can achieve a similar magnitude in test loss but using far fewer features and thus speeding up inference time
The test loss may seem extremely large but this is mostly because of the large size of the testing set and the fact that house prices are also fairly large (of the magnitude 10^6) and thus even the squares of small errors accumulate quickly and lead to a large final loss
As we can see various factors such as square feet, view, zipcode and more are often found in housing listings. However through data analysis we can identify which features truly matter to consumers (such as square feet, location in the form of zipcode, whether the house has a basement or not, etc.).
Using this data we can narrow down which features are best analyzed when modelling the price of housing using ML techniques.